FWS x _    ,C3ff  $1$PJ$YKfVxBL/7axjhmEu0ut1/1 ?   X 	 dTotalBytes this getBytesTotal dLoadedBytes getBytesLoaded percentLoaded Math floor %  HowMuchLoaded   i            R          R    d        R  G ?             HowMuchLoaded = ?    r!L 3 k{eA	] >~S6|'~8	cÆ\@IRWshl# ]^Su-ylц]@L	B*;	>5 M-GE7]c'"eI[/r l Qغѧ<>+J) d+7M[x<]:yβP-*=uii=3рX.L,=$JV3!#ҠR;뤫5;Y~79J{iü2dJ{ iS\(.Xl׽Vrgn.vd6[i6	S.wd,H)q7Q*RR@))WDaH+&dPO^ud'KkBZΒp97Du-0K 	(HEe!%ĉ`3dJ jiS)9=':П@ X)
 G`` y@'	 8~   ?b    VerdanaG      'mJuk{!<Yv"	A		
j

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w8/P 5Iy/<F*q 5M࠷n@ 5HybnQwg 5i{y7Ygbl 5jBfG _{*n	mfla	@1y勞- |Fa\Rwcu 	te+)DRYs L lw)O JӆǗ.hKW  5baJn5HmEM~N0 5jf G?qm"v;un6afCCE+ƪJf
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t(͖wd=5qn۴֬~Ҧo\u);Pͱ imvZϛ@`KY{D8dPa9[Nbұt0 5IfybnQwgTR{]u 5JVy/<F*q
Or<] 5ky,?ZμvȟP 5i ϊyxr\mz\*=T،'`-QKp2l΅}\ I6 XKܛn7@ 5O=^zT+qn
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L&(0 M} _Mw߉ϻNVcQ 5wi; &	]{vQ-MEů6Xӗw >dpQ]fsi_ 5jw"crj7#E# 5kx]a&}a*  mnqL @M1	2H ;s W 5lyF䯎ߞ]g>oF7<Ò "p@  5dLxWn]wIZI-pB`6Vp!),eԕ3Ųkt]4ہo;W{~Bdl5fJNHI 5 	\c[! .A 5ig@yMRku90nܩmů
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ـ-yؿ ,<A(δ 5hwSZiw4k\3\ lMZ 09TI ַvZnRͳAs[ bwu;ӷL  Xj:r׾A 5i{yXV3V4SX%-rRM4c?b Lp+)Y),Jr0C{Š*d\xnv:kkɷK  S%W5 5eDiȤPU0"yk@ \ѠFXf%=\O ..m|]rP 
*q/q˛$xܷv 5gs'5,I˴+zܽ'bfa7G	&Mf6o ڒ} 5i_k;}7l~Am#U{_"<󀻛ioB[ (~oS6RsZeaar|W*lt&`	O v[_5nɮ7
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	 .p+`P^P ' 5	 pХHRJǹYw^Ȁ4YMrdX ֿċp#Y1J'	rp&S 5ig@yzeYn'RZe& ]-v)|qkU7f &i :MJ28z Wrm˒@凒R(?֘N 5gUzk]oou#¼nRn~eJWsVpڣߠB 5hQKc,,@b$F (qr^28D w0!+{mk@VR"ЍZ5Ft ڷrkk>ͽim`
ܩɼ(knա 5akMer,B2%JHR n1/z`	4nٺ<7Ŷ6P 5jQ/VW)-bMF6vX'E p%%	F~$sv᜷ 5j.tc4n~q ' 5lr<1ܠhn<z?.~'Ƀ/Ϡ 5Nn*re޹FKyK[gQ@ 5Ju@R{!O7-^!ְ 5hwPܗf7Qb\eǍp%  5j3|y.5BllnI3z 5h X=j<I*& >Ę`eُO X̻RTt*1o
򀭗1-pː@  !"'()+,-./0123456789:;=?ACDEFGHIKLMNOPRSTUWabcdefghiklmnoprstuvwxyz  ^ZT--xrrxxR?Z/cg!@[^^<`c Z Xf&`  XT@XT 3Xa;Sg XS9g Xmau  P$PnͷP X>LQ X8T  XNX  X]T$  XFRT  X*V` XRR` XCT( XNR`  X2TX4R Xq%<  X')W<\X}_ XJH   Xa`  X4V$X_c`  X_OT`  X_N`  X4^T$ X__t`  X>>T`  X_b`  X_O`  X_m`  X_``  X4ft  X_X`  X_e`  X7Vt( XT`  XU]t` `  X+KXUSX,G6X-N X,OX83  X-Nj XUQ3  XP!  XUU3  XU!S  XU}V  XUQ6  X,Rv	 XUSg XU=4  X0G X7XQP< XQw<  Xz<  XT<  XQ<g X*GW<  XMQ| XMv| XZ@#U   	*    g2p0         percentLoaded 
  Y`@ ?U             HowMuchLoaded =  dLoadedBytes   dTotalBytes H           PBL 	 ̒     XN!̀ 
 ̒     XM!  
 ̒     XN  
 ̒     P>L 	 ̒    	 X!Oa  
 ̒    
 XN 
 ̒ 	x   b    &@4 i @ @   &@4 pi @ @   &@4Ti @D@   &@4TMi @d@   &@4T}@i @@   &@4T@i @@   &@4T i @@   &@4Ui @@   &@4U<i @@   &@4Uli @,   &@4i @ @   &@4U@i @L  &@4pi @ @   &@4U i @p  &@4i @D@   &@4M i @  &@4Mi @d@   &@4i @  &@4}@i @@   &@4ni @ԓ  &@4@i @   &@4i @ @   &@4.i @  &@4 i @ȓ  &@4 i @$@   &@4i @  &@4i @  &@4$" i @D@   &@4i @8  &@4<i @  &@4$T i @h@   &@41i @X  &@4li @,  &@4$ i @@   &@44i @|  &@4@i @L  &@4$ i @@   &@47i @  &@4 i @p  &@4$ i @@   &@4
ji @  &@4 i @  &@4% i @   &@4>i @ @   &@4@i @  &@4i @  &@4%N i @  &@4>i @$@    @4R  &@4	ni @ԓ  &@4% i @<  &@4|&i @H@   &@4
.i @  &@4% i @\  &@4|[@i @l@   &@4
i @  &@4 i @  &@4|i @@   &@4i @8  &@48Xi @  &@4| i @@   &@4i @X  &@49 i @ē  &@4|@i @@   &@4i @|  &@49i @  &@4},i @ @   &@4i @  &@4:i @  &@4}a i @$   &@4i @ @   &@4,*i @  &@4;xi @0  &@4}i @H  &@4 i @$@   &@4XZ@i @  &@48q i @P  &@4}i @l  &@4D" i @D@    @4X
   &@48t i @t  &@4u@i @  &@4DT i @h@   &@48w@i @  &@4,i @  &@4D i @ 	  &@4i @ @   &@4pi @  &@4,i @ܓ  &@4D i @  &@4i @ @   &@4p i @ܒ  &@4,mi @   &@4< i @Г  &@4#i @@@    @4p  &@4,?i @$  &@4= i @  &@4#Gi @`@   &@4Y@i @H  &@4=N i @  &@4#u@i @@   &@4Yӈi @l  &@4= i @<  &@4#@i @@   &@4Yi @  &@4= i @\  &@4# i @@   &@4Yi @  &@4= i @  &@4#i @@   &@4YXi @ܒ  &@4>xXi @  &@4#,i @  
  &@4Bi @ @    @4Y  &@4>y i @ē  &@4#Zi @   &@4B i @$@   &@4>yi @  &@4#@i @@  &@4," i @D@   &@4>zi @  &@4#@i @`  &@4,T i @h@   &@4>{xi @0  &@4# i @  &@4, i @@   &@4| i @P  &@4GGi @  &@4, i @@   &@4| i @t  &@4Gi @  &@4,| i @@   &@4|@i @  &@4G	i @  &@4,} i @@   &@4|`i @  &@4G
mi @   &@4,}N i @@   &@4|݀i @ܒ  &@4G%i @   &@4,} i @<@    @4|  &@4Fi @@  &@4,} i @\@   &@4Fi @`  &@4,} i @@   &@4FKi @  &@4XXi @@   &@4Fi @  &@4X i @@   &@4Fi @  &@4Xi @@   &@4Fqi @  &@4Xi @@    @4F(  &@4Xxi @0@   &@4X@i @P@   &@4Xi @t@   &@4Xi @@   &@4Xi @@   &@4X`i @@    @4X(@ 	 i @	 i @̉	 i @Љ	 i @؉	 i @܉	 i @	 i @@ 	 i @	 i @	 i @	 i @	 i @	 i @	 i @@ 	 i @@	 i @`	 i @t	 i @	 i @	 i @	 i @@ 	 i @ 	 i @(	 i @D	 i @\	 i @l	 i @|	 i @@ 	 i @	 i @	 i @	 i @4	 i @H	 i @\	 i @h@ 	 i @	 i @	 i @	 i @	 i @$	 i @8	 i @L@ 	 i @@	 i @	 i @	 i @	 i @ 	 i @	 i @,@ 	 i @ 	 i @P	 i @	 i @	 i @܉	 i @	 i @@ 	 i @	 i @	 i @\	 i @	 i @	 i @؉	 i @@ 	 i @	 i @	 i @0	 i @h	 i @	 i @	 i @@ 	 i @@	 i @	 i @ 	 i @<	 i @l	 i @	 i @@ 	 i @ 	 i @x	 i @Љ	 i @	 i @H	 i @t	 i @@ 	 i @ 	 i @D	 i @	 i @	 i @$	 i @T	 i @x@ 	 i @ 	 i @	 i @t	 i @ĉ	 i @ 	 i @0	 i @\@ 	 i @ @	 i @ ؉	 i @D	 i @	 i @܉	 i @	 i @<@ 	 i @  	 i @ 	 i @	 i @p	 i @	 i @	 i @ @  	 i @ l	 i @ 	 i @H	 i @	 i @Љ	 i @ @ 	 i @ 4	 i @ 	 i @ 	 i @l	 i @	 i @@ 	 i @  	 i @ 	 i @ 	 i @H	 i @	 i @@  	 i @ \	 i @ ̉	 i @$	 i @l	 i @@ 	 i @ 0	 i @ 	 i @ 	 i @L	 i @@ 	 i @  	 i @ |	 i @ ܉	 i @(	 i @h@  	 i @ P	 i @ 	 i @	 i @L@ 	 i @ (	 i @ 	 i @ 	 i @,@ 	 i @  	 i @ l	 i @ ȉ	 i @@  	 i @ H	 i @ 	 i @ @ 	 i @ $	 i @ 	 i @ @ 	 i @  	 i @ d	 i @ @  	 i @ D	 i @ @ 	 i @  	 i @ x@ 	 i @  	 i @ \@  	 i @ <@ 	 i @  @ 	 i @  @     )@ HH  @ @ @ @ @ @ @ @ @ @ @ @ @ ?      @   
 ?Y   "  txtIdentifier Math random round            R       R 
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 f%Ia?2`Cw2{-  *    X\b f ,W{'Ȃ [, ?     VerdanaO      6{R|sm#@\sJk	1	i					g

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_ebkf_a 5NR\wջfs!b_~c_o۳&1 5gd]{]<}[@mJF1*Do*JIk,R/&Xf (K]rC8t@-nz@dRmkO{rgnp%Oiy幺]}[dEw` 5f)i[v.`SJDTiWq&H >ve\pf W_t}ӟ6-ܶ R[5pc1~z'<|@^;I%ușaMl>  5fnlQݯҵ$00L<83
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 tttv,v.vavevovvvvvvvw,w.wawwwwwxcxdxexgxoxxxxxxy,y.yaycydyeygyoyqyyyyyyyyzczdzezgzozqzzzzzTVWYTVWYA,.AT7 V2 W Y7 st A,.AT7 V2 W Y7 st AIJSTVWXYZavwxyzAIJSTVWXYZavwxyzAIJSTVWXYZavwxyzǌǖǗǭ,.TXYZ؅,.vxy$    ` " 	 fwnvMl  *    X\b  33 Mnodw`qOu $    ` " 	  33wnvMl  $    XFo@   33  3f5m|d+@      |       u@Dc       34  
B    u@Dc 34  
B    @@'t@
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             ì       PnH 
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 	  33wnvM  $    Xy@   33    5o |d+@ ,          @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
         @-Wa      Xg  	 f|Mf      Xg  	  33|Mf  .     _e@   33    =l}	4#KN ;    !       @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(            !   @-g     " Xl!   	 fnn     # Xl!   	  33nn    $       @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}          A   $   @-uY  &   % ]_]([   f f%t Z\4Bp   % H &   & _a   f f%l0\+A$9  &     ' Wԉ 	 fB@  ' =F    ( X!@z 	 f  bf	  ( @ORwP &   ) o__   f%7fa5Y ) ;     * @  3ff% 
   *  4   + hP   	 fvMnwljnvM  +   @'U    , b6  	 f  &@   , 0O   - p   
 fjhRz@(uah=@ґfxk<5fUuXx  ! -  @ k(" *  3U  . t>jT = Ԉeh   ;o.o  {u  d 4o)  ,q =g[k  Gw  'sh %4|y8  ,@P;&j C\@svr  iI[  K@PKb@  < 5"poe.  90t.}  @E@  q @@c[拖   98l0ݾ  HHH+aS7Zo- HHHWWW k*@pQ HHHWWW IO  ,h#-| l/  rrruƌ@'~`  $ >@K{|   \$ i8  Rl@0=ؠ  y@h q m/;     $$$TTT P #hJ  T _1 III Pk #o ,@PJV  B/@&  u uh  "fRB +%  bS
lC  HHHS-"@ S3 " OVzO  tᏪVsa '\ota \O{ uuus4  vvvyk͞	> ZZZxxx$Ox| ZZZvvv*ɟ0 uuu6~F  &&&<<<(E0@ uuuрD  QQQZZZlџG<  ZZZuuu՟D@ QQQZZZﺶ{  uuu<o| ZZZvvvjɀi; ZZZuuuYofzԋ ⯺u\ ʴȹE'  e$~  QQQZZZ{NGf gvfN 7?'  2+Kٛ/  }Ke4  vvv|rgN xxx*Kq)-` :!;+-` rkfD |O6mtN m\/gΰ xxx=!  3۽ @ o!  HfSh ]]]1zRSg<Q8 [[[|||
=o_  VVVmmmOg T TTTddd_OVgAը JJJVVVA!7T  TTTddd[vqg\R SSS]]]A.fSh ]]])\Jg  LLLYYYcPVgAը JJJVVVs5ʝ+fԀ qDf8 |||W'UfX ddd!})R@ c YYYyyyT6h  mmm  ^^^]j YYYyyy)Yt՛j  HHHSSS'
ćfݠ HHHSSS{	p)ywk OOO^^^+\gX  LLLYYY3pk OOO^^^ ӻ5 r HHH[[[1"f׈ VVVmmm@	g mmmIY dddCSD]o` SSSrrrTfQH ||| .?ٟH HHHQQQ|M!  HHHRRR -ՀH HHHQQQ+v{-  HHHRRRۺٞJ HHHSSSO\~  QQQZZZ'f̌gYR SSS]]]nӮ)sF@ RRR[[[#ۻJ HHHSSS{hTgz IIITTT|h۬gz IIITTTnoӭsF@ RRR[[[	n'dg9( [[[|||%> ZZZxxxQzfΐ  b( 4ae  b [SdeĨ   ;ZeX  b KZe  j ;eF $ Zeϐ H󜥖; P2fL }*
fL` e~Wf>O@ cqʋf=H PƺeQ   Z9ep \ħffp   5fS  Vؕ 7weJp  b _O'eʘ  Xc =oedQ 0M>eyUX Ske{  9lEy7 	]  2; Q``  ѻYD -6ea0 ,NeQ =e7b  /ex0  @ 2}` O-8e8` Aqe EU  D :rUC q/f,VP Q3gfa0 He :(eW  O@Eӕl@ sZQz ;I\u l_e  2+yr gFd  C}2eS =͘Z  ^1ega 0FeY 3蚑e Պb܀  b GkeL CdffR( V~ep - beސ Lƣaqu  *

$!rL uH N[MG\   ?x;- G?v\  RELe\z  л&W
 ~sJn  gxC&\  Md%o  Z-pv  Ըjޙ Qw'\@  (Me.i0 DKedc8 CS! "P= ŷ*e*| .e-i V\ ,9e[ $ՔA :, ze78 +&e` @eD  e3X ||| e+| HzeM v>$YRd ] V\   є<` ppp  y rrrUj$ Ud%  +[  yqO  jp&[,  	+[  } ip\ 9&<e 55r3    Wgg@ ^^^hhh&QxT]=  [[[Yos5 rrrw	r鍚)} ^^^cmQ.X] rrr3VxD HHHpppE [[[9goqu HHHpppkEl  SSSrrr9׼eɂ pppV	z=s oe+,]5  ppp uL ~~~}qv  HHH[[[= 	^@ hhh~~~? 1]` ggg{{{?  W`| ggg{{{  hp ]]]ggg  hp ]]]ggg wQ= {{{ 9EOj {{{ 9s   yyy5	5a|  yyy f5\   dZ     $$$ j\/V    -Dho    $$$Yv  5553 ɻk        #|ru$dh.( 333EEE^Wԅ $$$5555|&  555EEE  q	mx """MMM Q,hR4 ===W&` ===  1kh """MMM  MҠ %%%TTT?@P   , * ###ccc : OhG &&&ccc1CӇ5` ּ ="` &&& %+q  &&&݋7r qqqbgT| ===cccz4AVԀ   ===MMMjM˵ MMMcccw.q<g0 TTT*E`   K_     q v!G 1 # qqqA1( 5551?\I@ HHHQQQ Y  `R HHHQQQE	&
|D &&& V$Ӏ !!!( < ###JhsGH  TTT ޻A*& ### v
̋ ### xP`Ԁ ???
|% !!!̊  DLX+ !!!u и + !!!.3s? HHHuuu  AY1 IIIe X ???III(p`  ???BôT`:Ā IIImSK}cB    HHHiT=b    .ˏтD ???W ;?`%ڀ ,,, L   7iq   OKǥp  \gcMg  ջcՂsc     x6z`hV &&& R` ;<O~ &&&Z?XD    HHH	w݀f 111g  `Z@ 111n2' WJ6%~   7W/v ; "A	g ҿ{ yKɂs  H4`( LxQ  &&&HHH ߴ whn $$$TTTǝ 7+  .u& HHHuuuAPsD< TTTkkxk8 qqq  Wړ ]]]fffA  Wbh fffyyyC v!  fffyyy  ]KF yyy u- yyy  <` ppp8_I ]  Xe;# yyy e3X ||| xe< yyy  M  mmm|||JydU> fP4YS` [j ] qajw (\9 @q.` /і  eབG iޥF +'D 1 @ 65BH` s}Q, &eͬ  c	/͖H  1 Mkke,H c qdn 2f; ~~~+Zf=, ~~~q,e ;̤Uf, @`f, QN» e xxxVƿze  0 >e  1 ɔ  5 
7e"# O  k[JI@ " U F ڮQr   j t#e*( :  ]  "P  י ud, 5\fI
2 >JvQ:  wViڬ )QJ  ;0Gjea(P  
 !@ ,-	f &MY
  м Se  6j JxdU>  ĻvE`	  Ce8  X&Ts  S ~W )FWk  [	ٕ6  eRQ  wiY 3 &ɠ  Tz= 3)-z;d 3F!>d߲`   u@ WIF  % d 1RD  ?fR ;Cޣe` k>`wdغ` m5Ȝe3 1		  0Ke` ~~~.e5 Mķeg wwwF̰ef wwwYIh o5e= y!Iɠ 7~
(d4 Q2{6RR  Le@ #I}$f,P hhhxxxJδf'2 hhh~~~K>`f9h VVVhhh;
3fU VVVqqqL趍eθp jjj~~~He8p jjj~~~C>\f19@ NNNVVV[JwZf2@ NNNVVVFXAe> HHHNNNe&hfV8 HHHNNNAe2 xxx7,eP ~~~If9  VVVjjjNkθce xxx'P"f  VVVjjjo*ef LLLVVV@@ 4e@ 0Xb׀  2 1Nd, P^޺?e=H ```www=f(0 hhh~~~ 7*qf0 %,*fl,P qqqY_γ@ qqq jP vvvkʿvk8  QQQsssaY]^@ [[[sssl^	ܪ HHH[[[9 $%ǹ VVVqqqyy{Vi HHHLLL'lf}2X LLL[[[ +I+\J  Nz\J`   nz=!5` $$$jjj Go7@  www 7]7  www a b׬` VVVckAt^N9 g ktↀ   u%ؔ  $$$jjj  j!r/H &&&mmm#Un   m{ VVV G [3]4@ 666Y,ec΀ VVV"s" ٰT 000XXXJ qKwd8X 000<<<QI]3 )))<<<dݐu  $$$000 `ʏ Kcvm ###mmm Tt =kgm ###mmmB=+mK
 ___'Zf`m EEEuuu+\^m EEEuuuEQ\6.d` <<<XXXI \m֊X FFFuuu vL@0| FFFuuuW	| ,P ___Q Wm獔 鹹o6 )))III  Lm ~ͥ4p )))EEE)Nmm͈ )))EEEoE(m挎 )))<<<SY  QmM s  Ld@ YQ Qdx TmrMN9 )))III  ud/2 ܱ @|[j  mmmRJv$` III%D` DDDU`,=p )))IIIokdQ  ;;;WA< DDD;V@ )))III]yٷM9 )))IIImDmO( HDm )yٷ5 III7MZ/ III N_ 4e
iJ  jjj B _.NdԯH  8 1Yd/   %o a@  H ]6d1  )<"T`  !k fRĠ   1d3@   #,dt4 2 {M[6    }Odɱ0   Ed3@  k$f풴   4viʀ m71IX ((( V @U  c  Pd  |  OdF28 \A  )))000 g e    6b
   6el  q/7->Π  a!-@  .Vd: $$$))) ?t2נ  )4%M qd Q  nk#n  \&iנ S|½#d7 E3Z   Nb  ἟e` iRdǷ e)Rd< F?Y	O l5 jjjzD8 LLLp d? :?c a%A aBx lllă-A Z) m  il/B [ŸoC  XD?ۇt0 %d9L0 ''' xK ''' T?[$  HHHMMMz&1?[䲀 HHHMMMpoV9" NNNeeen5R0 NNNeee[ϛD MMMcccF>nBҦ HHHNNNu'͹~G  PPPhhhԼ쏮 PPPhhhy6q eeeֈŹ>D hhh2ŹDD hhhm-# HHHPPPOޅJx HHHNNNα?ۊ4c  eeenn) AvR[r )))DDDH>m
 >m hq?/ XmP ʛ}T9 %]Z A( )))DDD5eڹ. ///LLL^_A ;;;{ZmP  	%E@ (((;;;o{m cccq/D (((;;;?6ܩ"  (((///:q:` ###///)[i$ ---LLL [uD MMMbbb 0?  MMMcccoIP  ###///ջ#ӕM@ ###(((&Av ''' T'1Կ[w  HHHMMM)9km '''`@mT4 '''%)mT '''?m ''',SlO ''' Ԫ[tf bbb;kk ccctm ---LLLѱqED  [<Q      o뎑.PX     ,ɪmʔ  sQ ###!m ---(/B+  -ܸmR ---LïK6- fffLٯm LLL y{. 666ȟm^     zei(  HHHLLLBCܯK48 HHHfff Ra,Q     #Zm 666XएmT    *5eP8    682 m 666VVVfE\̳e HHHQQQYK,X5e HHHQQQ 
i Kan  
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   G<  N O  N O  N O        N R >     inputString      R<  	         N !N< "        <            	         N #R $I   "   < %  " &%         'R< %    ?	         I   &&     &	         IL   & I >  (             	         N )R< *(<  &    I   + 	                   	         N )R< (                 	         N )R< *( ,G +G< 7 &    I   - 	                   	         N )R< +               	         N )R< (.                	         N )R< *( ,G +G ,G -G< ? &    I * / 	                   	         N )R< -               	         N )R< +        	       	         N )R< (. 	               	         N )R< *( ,G +G ,G -G ,G /G<             N !NH   ** G     NG *>O     num digits  0    1=  	         J> _         2H <  30     4RK< 53     R< 5> 62 
       7R< 30 6     4R 6K<	    3 8R I   33 9G :   3 R< ;2 :    N !N< <   < ; <H   33 =G <<P  53     R< 5>O  >   num sigDigs . 00J 0    1=   0> ?0     @R     AR	 k@U     'R< 0	         I   ?         6? 
       7R< B0 6< BC     B     R DB< ?	         I   DD E?GG D>O ?!     pentax   FreeToRotate  O ?E     cal _visible pentax element    O  N  O 

   calibrate  ?   vö  @ Pmz 0   V moD  3ff m,z$:,jpQ!D+ 	   W   *  @    N   X ]C 	>  333ˮ] fff  w=(qЇ7yW`#  #   Y _t_  <   <  < %n |  +   Z Ulo <   <  < < %V8S 	$   [  ?     Z  @ @ ?    @   	/   \  ?     Y   [   @ @ ?    @   	9   ]  ?     Y      330  [       330 @    6   ^ _t  < f<   < < 2< 22< f$ynnx 	`   _  ?     ^   @  ^ o, kZ8@ ^  Z8J  ^ #]@ @ ?    @   	,   ` g"O
P1           sStress -000.00 	   a  ?   +  dStress sStress  Math abs formatDecimals   	         I    9         R	          R  ` ~@Kʢv@ @ ?    @   	  b  ?H   flag_sigmaX flag_sigmaY flag_tauXY resolution sigmaX Math abs sigmaY tauXY blue_x_left blue_x_right green_x_left green_x_right blue_y_top blue_y_bot green_y_top green_y_bot tau_positive tau_negative dynSigmaX _rotation _parent pentax dStress gotoAndPlay dynSigmaY dynTauXY   A A A   ?    <      R H        1          H                    R H       1          H                  R H       1          H                  I 9 	 	  @#	 
  @#	   @ #	   @ #        I 9 	 	  @ #	 
  @ #	   @#	   @# I       I 4 	 	  @ #	 
  @ #	   @ #	   @ #     I 9 	   @#	   @#	   @ #	   @ #       I 9 	   @ #	   @ #	   @#	   @# I      I 4 	   @ #	   @ #	   @ #	   @ #     I  	   @#	   @ # c      I  	   @ #	   @# /      I  	   @ #	   @ #           N N NO      I            O    O        R           N N NO     I            O    O        R           N N NO     I            O    O        R  X     & \   blue_x_right    & \   @   blue_x_left    & ] 5 green_x_left    & ]    e@ green_x_right    & \   @ blue_y_top    & \     (blue_y_bot    & ]  5green_y_top    & ]   ʀgreen_y_bot    & _  tau_positive    & _     tau_negative    &$ a @ rdynSigmaX    && a @ HdynSigmaY    &( a @ npdynTauXY @ ?    @    V   c Un*@ ff ,7qSSV"\WItjݺ恵wU@f4o3X>&Z  5   d V ff ̙3  >ST%8Uqi SoԷ`h0    e  < c  Mc  M    3 c  M    ?0 d     H   pressingRotate        FreeToRotate pressingRotate              f TX   !kOREZAIڑRE@YHURTiPVվ
#QVJڷS-p?XԭQVT:jԬ
Z˝Jڷj$έEZu+REZGS^ejk,꽶REZALUm[ખ5PVտ-:jԬ
|C8S\UR).u+jURƪJڷ0UR     g T 3 Rk)o$     h dm9/      KW^X     i TD f   My-\6#^K     j TX   Rkk,$    k  E f   g   h  УWҫKi @4i   f       0 j         FreeToRotate  0   snapshot  txtTheta   shutter_tripped      l X cش     %@ٻiH n3 	$   m WZ{ 1 <          txtTheta    n H   & = < X 	&   o  ?     n @ @ ?    @      p A{   . = <  	&   q  ?     p @ @ ?    @   r  r e.*=`   333    ~O     zM 8M8  ( Rrr( 2EE 2EEBfQ	`/"h7HqxF =t59	#TvY|_zro%"覹log>V .v:ST-l(ɥɎ.kgscz-7nWV&\B
Q^PNݏnY?]A/tlt`'hd:#Ȫ	;HT}hLPu^$U*l2}esKJ5c[y^q*k t.䨀Y.Ge;[kNk̓LI&$Aؔ@M}NG4ʧzcf,ǝ5sPzsJwqly' 5/ELkRA/#\	@r5o9뚆I@8vST=s.	tu+SFWo   K K 333K fffK {%n_5I,1&ɯ  Rjcy |0qG
 M2D9 D>Y 	   s  ?     shutter_tripped   

   activated  V     . W  3 h    regMark  =   @
@   & b }Z0 element 0 e 6lMU 2 k 
:rІ6 l  7 m /   &8 o n    &: q Ht = r  @ @ @ @ ?       @      6 s uR  pentax -   t `5p" 	   #bbfVSlЙ% 	"   u   t   @'	U@ ?    @      6D u ,;  cal    v x t S 
 f=V0. `vE) *`Zb;"oH `] C 0-1!x`pc1 -t^b4@ `z@31@    o;xS= l3t 043t `fc0me;X] 	%R` pc1 fӲ- `\R.  ")0 `^b4l+pc) F v 
QG   w hP   
 fjI3*	օtAəQnnS΋8$̨~7)Lʀ I w   @'U    x b6  	 f  @ J x 0K -  @ k(h    L  ì  6  y  )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
           Q y   @-Wa    z       @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(           X z   @-g    {       @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}            ] {   @-uY d % He &  f ' =F g ( @ORwPh ) ; i 2 @ TtsP @ @ @ @ @ @ @ ?D     cal _visible pentax element     O  N  O @ @ @ @ @ ?D     cal _visible pentax element    O  N  O @ @ @ @ @ @ ?D     cal _visible pentax element     O  N  O @ @ @ @ ?D     cal _visible pentax element    O  N  O @ @ @ @ @ ?D     cal _visible pentax element     O  N  O @ @ @ ?D     cal _visible pentax element    O  N  O @ @ @ @ ?D     pentax element _visible cal    N  O   O @ @ D ?k     sigmaX 
     sigmaY <     tauXY <     theta                      SetupTheElement = ?*     pentax 	  element N  _visible O 	 h#H 	 h#H  *   | }&  f %M  }/fz5 /fz4  |   ?N   } P 	      }   ?r`   ~ P 	      ~   ?JZ u#RH)    `/" 	   	OrGfV)6`` 	"         @'	U@ ?    @      6D  ,;  activated :   x 52 S 
 fC2ldXqJl04ȵdb  "M3 fc.
g-txS0. fc.K 0B-F-tz@4w0q fc.   oA\R.ۥdZ X]1LFz@,.ސ   07JK3 0<)ȶLxS p 090vӲ, h0;"KWAɀ2 F  @ @ @ @ @ @ @ @ @ @ @ @ i ?    G h kR@V    c1     pz" 	   Hrzm`*a ZlR|` RXvwvwrx R. Rzm`pxhRrp Rxzmvw`xx 5!dvw``p RXvwvwrx R. R\rntvw`xxhRrp Rxzmvw`xx Wvw`^ RXvwvwrx R. Rxf`Xvw Rxzmvw`xx H  1bai ; @ TtsP @  D G H L Q X ] d f h i ?     pentax   FreeToRotate O  sigmaX 
     sigmaY <     tauXY <     theta                      SetupTheElement =  !߀  `	     ?     shutter_tripped   

   activated  V     . W  3 h    regMark  =   @
@   & b }Z0 element 0 e 6lMU 2 k 
:rІ6 l  7 m /   &8 o n    &: q Ht = r  @ @ @ @ ?       @       u#RH pentax   B @ #  F  theKey Key getCode RIGHT UP this _rotation LEFT DOWN PGUP PGDN HOME            R<    NIL     k   IL     +   IL      NI *      A N	 ?# 8    NIL     m   IL     -   IL      NI *      A N	 ?G#      	NI &      A N    # p     
NI &      A N    G# 1     NI       A        #      element gotoAndPlay pressingRotate point x  y _parent localToGlobal reg regMark _x this _y deltaX deltaY initialRadian Math atan2 _xmouse _ymouse rotationRadian rotationAngle _rotation SetupTheElement n t          R  x         "	    "    C      R 	
 N  NG  
N N  NG    C 	 N  N 	 N  N       R  N  N  N  N       R       	 !	@-DT  O  N     R           NO           NO   ?"    mo         tWbWX D        h   	    B`ZrXvc^ D\vrpz[vcrlDxwf  LXd`Tt    _LXd`6rp  <  >rn` E   @ A@b    `! 	 f  Hu  Hu Hu _Hu  <vc`xw`z[ F   @ Pl    m3*"U f eR~YLeGaUFʎٹ`eQ6˶noaGfoQC  f OU*;YfMH        x d AT 
 f9R_0 ȷ&av`] C2╩x X]1טe#-av 0= ɀZb6Bff;av`]/1 d[-Ɂ 0    oxS6&"Hʄf4 0 ȸE 090H ɀ `db0. `]6 Gg&, r`@DHf; X]JNȵP~[0.FP I  
QA    hZTP   
 f;*ʈsr ntX)MI&eCAOrfT  J    @'U     b  	 f  R	 K  0L -  @ k(h    M  ì  6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
           R    @-Wa           @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(           Y    @-g           @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}            ^    @-uY e % Hf &  g ' =F h ( @ORwPi ) ; j 2 @ TtsP @ @ @ @ @ @ @ @ @ @ @ @ j ?    j ; @ TtsP @       D E F H I J K L M R Y ^ e f g h i j ?K     virtual1_attempts                 virtual   gotoAndPlay R 
   virtual_one   ì  6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
               @-Wa           @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(               @-g           @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}                @-uY  % H &   ' =F  ( @ORwP ) ;  *  K    hP   
 fS;b2 bnS)x5 ܧXPJr     @'U     b  	 f  R)    0! -  @ k(" *  ;    p 	B    B/Ɖ<Wp|    ]$<   $    DP     [[P6LkbT  %    F     eݧP2ũCvu  2    FU@     WU9k3#1.x>Mԡs]gcvCs@  9    F\      Y\ТIY7b]Hsw[4  <    E%@     n,犴4ekfQD4ސ٭`  n    E%@     GOP9hum6UaʖÎ3",@/7I_.b4NĹ?`~^=ȬV\ =  ,    Ez     	zU]H
V;sU  /    E20     z^
)ԍnn+=hm@  a    E\8     l{ͽ:(¹:#A^>4V_P b@ 3eRQvjnɁ""l:x  a    EUX     K"doMm9e	_;h^ʣ@g\P켺d~K2y .AC]-k/dΑ#k8  V    DU@     #d;%ҠrNƥI ^2忎W'F
w9| ^۞^3yv:S  :    E%@     J6|<LV۞cvCDD l  X    Dl8     &d#Z@8=`$\쀦@*2ƐC_^Gez	hÊ\XTSإ?x	U :^S#      hF.A  (    %d|{8      h4  (    %nz  	e   3 ?     h 9 ,*@ @ 	 i @  @ @ 	 @ @  9 -"*  gp@  9 -G  p@  9 -w*  @@  9 -  @  9 -򪐉  RX@  9 1 
  RP@  9 12ʤ h ]@  9 1F@  9 1s	  d\@  9 1J
  D@  9 1
  d@  9 1  @  9 5  @  9 5  \@  9 5*©  $ @  9 5?  !$ @  9 5SB  A$@  9 5]   @  9 5g@  9 5©   @  9 5  !$@  9 5B  A$ @ @ 	 i @  @ @ 	 @ @ 	 i @  @ @ 	 @ @ 	 i @  @ @ 	 @ @  @ F h =t    @  @ d@  @ 
@  @ eD@  @ c:@ F h H    @  @ 
ڐ@  @ 
S@ ?     @ w@   _   p X  
   fR_1@*PvE.0\R1   or`81L; h081F#z@ p  tb4 0.)Vmz@0.A ǃ  z@31@3xS<)O
`A `z@31@%av^b   n[ d[qJh090
a#(  	Nm0 fc.UttX]L ٠^b   m
z@31@`]<) `] LdXav  Zb6r`@D pc!L81ul  b;90u  `] d[#tz@ te  l\RV  ` 0      r` l+ 0=   \R.ۥdZ pc1#( 	   < ?         @ P        ` @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?#             _parent   play R     @D؎  h MDy! h ;ÅK    " f ř8^d @      6#  á  virtual F 2 @ TtsP I *  @ @ @ @ @ F ?    F ; @ TtsP @              ! " # F I ?!     pentax   FreeToRotate O  ?   vö h#H  @ Pmzh#H  |   ?Nﰏ }   ?r` ~   ?JZ	     ?     shutter_tripped   

   activated  V     . W  3 h    regMark  =   @
@   & b }Z0 element 0 e 6lMU 2 k 
:rІ6 l  7 m /   &8 o n    &: q Ht = r  @ @ @ @ ?       @       uR` pentax   B @ #  F  theKey Key getCode RIGHT UP this _rotation LEFT DOWN PGUP PGDN HOME            R<    NIL     k   IL     +   IL      NI *      A N	 ?# 8    NIL     m   IL     -   IL      NI *      A N	 ?G#      	NI &      A N    # p     
NI &      A N    G# 1     NI       A        #  K    shutter_tripped shut _parent gotoAndPlay element pressingRotate point x  y localToGlobal deltaX _xmouse deltaY _ymouse rotationRadian Math atan2 rotationAngle this _rotation SetupTheElement n t    I  	     R        R            "	 	   "    C      
R  N  N  N  	N       R 	 !?(-DT     	 !	@-DT  O  N     R           NO           NO   D    E   @ A@F   @ PH    8   x @S 
 fA:[4@ 06nȶF#L 0?-m; vr`;"`] nȷd[$ `ZbB-ȷ&avh0813t `\R.ۥdZH ` 0   oB4eV `]       ` 0   ɀ 043t `~[4P&#A`];"H& \R0k@"ɀvEl3xS	@ I   @'J h MD)K h ;ÈrL    L f ř8g$X    pM
  	 f|Mfwrnn bf|Mn bpbw bf bh|Mn bfww M    @'U     b  	 f  RI N  0O -  @ k(h    P  ì  6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
           U    @-Wa           @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(           \    @-g            @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}      a    @-uY h % Hi &  j ' =F k ( @ORwPl ) ; m 2 @ TtsP @ @ @ @ m ?    m ; @ TtsP@ ?a   7  virtual1_attempts snapshot_rotation pentax _rotation        G  N  
   shut @       D E F H I J K L M N O P U \ a h i j k l m ?    rotationRadian rotationDegrees thetaRad deltaSigma sigmaX sigmaY center cos2Theta Math cos sin2Theta sin snapshot_sigmaN tauxy sin2theta snapshot_sigmaT snapshot_tauNT cos2theta polaroid element tauXY gotoAndPlay _rotation ) SetupSnapShotElement  rotationDegrees }  	 !	@-DT    <          <      <  G    <	         	R<	 
        R<   G  G	                 G  N O  N O  N O        N R  N O > ?  ' snapshot_rotation SetupSnapShotElement snapshot_sigmaN snapshot_sigmaT found_green_arrow Math abs snapshot_blue formatDecimals snapshot_green txtReadings <FONT COLOR="#FFFFFF"><U>Measurements</U></FONT>

Camera angle =  camera_txtTheta  

<U>Arrow Magnitudes</U> 
  Blue arrow  =  
  Green arrow =  
  Blue arrows 
    (greater value) =  
    (lesser value)  =  NeedToTryAgain tolerance virtual1_attempts txtComment That was a good try; however, you should be able to find a larger value for a blue arrow.  Go back to the previous scene and try again.

<FONT COLOR="#99CCCC">Hint:  The angle should be about +56.</FONT> OK.  You still haven't quite found the largest blue arrow value, but give it just one more try.

<FONT COLOR="#99CCCC">Same hint:  The angle should be about +56.</FONT> Well done!  You've done a good job of finding the largest magnitude for a blue arrow. Although you didn't quite find the largest blue arrow magnitude, let's go on.   The largest value for a blue arrow is found at a camera orientation of +56.31. <FONT COLOR="#FFFFFF"><U>Measurements</U></FONT>

Camera angle = +56.31 polaroid gotoAndPlay 

There is a special term for the state of stress you have just discovered.   These stresses are called <FONT COLOR="#FFFFFF">principal stresses.</FONT>   The principal stresses are the largest normal stresses that exist at any orientation.   For this particular point on the pipe, one principal stress is tension (blue arrow) and one stress is compression (green arrow).   The <FONT COLOR="#FFFFFF">principal stresses</FONT> always act on planes that are 90 apart. 

Also, notice that the red arrows have disappeared.   There is no shear stress on the principal stress planes.       =  	         H             R      RH e 	         R     R	 	        R     R ` 	         R     R	 	        R     R 
G G 

 G  I 1  

 G G 

 G 	G ;  

 G 
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 G G 

 G 	G  ff?ffff  	 Q@@     R H      	 (^@\     R H      	 'L@HzG     R H      	 Ib@RG     R H      IL       H    W  IL       I    !   I       G    'LHz      = 	         R     R	 	        R     R 
 

 G 
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 G G 

 G 	G        R   I i    G  !G  "G  #G  $G  %G  &G 	    ?    
   start_to_develop  h soЪǔ     (
  h soЪn    : F h őC   ? ـ   .jZhs4  @ Pڦxb2hs4 F h őC   | ř1	 } ř5ؙu
 ~ ř43F h őC 6    & b ř1element F7 h őC 9 8 h Œ>3      @ @ @ @ @ @ @ @ @ 8 őĳ  @ 8 ő  @ @ 8 ő  @ @ 8 ő@ @A @ 8 ő@ @A @ 8 ő@ @ @ 8 ő#  @ @ 8 ő3@ @p @ 8 őr  @\` @ 8 ő\C  @0AP @ 8 őC  @ @ @ 8 ő(@ @  @ 8 őS  @A @ 8 ő3@ @P @ 8 őȣ@ @@ @ 8 őc  @ @ 8 ő{@ @p	@ @ 8 őQC  @p @ 8 ő$#  @ @P @ 8 ő  @ d 0 @ ?    
   fin 8 ő# i @  @      6  f9|S polaroid 	    wp@3 f         txtReadings <P ALIGN="LEFT"><FONT FACE="Verdana" SIZE="14" COLOR="#FFCC66">Try to find the camera angle that reveals the largest and the smallest values for the blue and green arrows.</FONT></P> ;   @'
 	>    ' 3  f         txtComment <P ALIGN="LEFT"></P> <   @ \    pK쀊
  
 fS;b2 bnS)x5 ܧXPJr wnS$/tRH =    @'U     b  	 f  Ri >  0? -  @ k(@  ì 6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
           E    @-Wa          @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(          L    @-g         @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}           NeedToTryAgain   I   + Q    @-uYX % HY &  Z ' =F [ ( @ORwP\ ) ; ] 2 @ TtsP@ @ @ @ ?   :  polaroid element dynSigmaX _rotation dynSigmaY dynTauXY    N N           N NO   N N           N NO   N N           N NO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ] ?    ] ; @ TtsP*@  ; < = > @ E L Q X Y Z [ \ ] ?/  q 
 snapshot_rotation SetupSnapShotElement fin polaroid gotoAndStop element dynSigmaX _rotation dynSigmaY dynTauXY       =	     R  N N          N NO  N N          N NO  N 	N          N NO    6  f9|S +polaroid \    pLj
  
 fI;\bkؚԒfT@,ZMp bnS)x5 ܧXPJr ?    @'U     b6  	 f  R @  0A -  @ k(B  ì +6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
          G    @-Wa+          @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(         + N    @-g+          @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}          g S    @-uY+Z % H[ &  \ ' =F ] ( @ORwP^ ) ; _ 2 @ TtsP+@  ź,9Ct @ ?   :  polaroid element dynSigmaX _rotation dynSigmaY dynTauXY    N N           N NO   N N           N NO   N N           N NO  ŧ9#U @  Ŕx96 @  łL*9@@  o9@  ]
9ـY    p 
 
 Pcv٠X]1 `8_.d[APpc  	N; ;   @/
 @  Jj<9ϲ@  7̛9ے@  %,9|@  O9r^ @   9R? r   piJ 
 *c@ i3t 0@D@d[ z@0.Hf; X]JNȵq `] LG3`]  o*^b4GfӲ-tz@ LBX] L; b; Hd[L`]<)8 `]  'tb4#( fc.
g-txS0.3av 0@D@&-h081m" *n0.o
g;-t 043t `]nu l `^b4l+pc)	 t$e2 n+z@31@*`Zb;"oH `xS= l3t
L  z@ uۃ2  $R_1@& 0= ;# fc.ސ +3avdb0.L `r`>1ݑ` 	~[4P& `r`;";avh090FP <   @ L@ @ @ @ @ @ @ @ @ @ @ @ ?    b 7 ܨB@ b ?    @ @ @ @ @    x@A  
 Ac@ i`] 2ɀ`];"K@z@ vӲ-t `X]"@+PvE.
f `xS= l3t 043P 0 o=^b4l+pc) `z@31ܘvF#3 fc.lIt`] L ɀ(tb;"O
g3Aɀ 0<)ȶLxS p *r`>1ݑ`&-h081m  pc1 `av`h0-1kAɀ 0<)ȶLxS	@ =  48@ @ @ @ @ @ ?    b 7 ܨN@ b ?    @ @ @ @ @    & ( 9  P$?W 5HybnQwg 5gf P	!fHMKf6- M\lf(?}+xƅS# L M*}@+im3Ӯ~Wt7.pK 
 H1bޫ ӀCL՚M6E  5eB )H4֞/۔cjJrmSbZ@AJTdCzߜvSo_m`3~kv'1{vѸ[n$@dՌ $h 5hVd-amքo|5Xa٧r|` \͠fYF+,WY=PY-p&4ϘE'dEP 5k{yK:6G1s\6~XWSJ[3p mP
;PTP;tW(E` 0zc@u箷jN[! 5fN~ ?3 Pށ/dKJҔ3J]؟F	f3l d ˁ5cXg]2/" *9Ǧ}rD@Z=- 5geQ9t/+o+2R.ŖѸgs廀mM>'] 5f{w;˟Ͼ_1s 5e{yK-' 5iveLd{	z%k		f'$ D)kn+tk#XZǕp
ܤnbR@")xr]Z1۔b
-}+{k6J[0  5if*$ FIxn+uk/XJÌxr	KHnR+-*n L TJ 5ifC; h?nd])& k@	i-Fo&1̘9d^%`	R%KR?| c(FLh {|){+.,rO-	 5jK_zT	5p\` V9p[*TBH,=&ϸGe/E@JqCR2 ޲9.vZ /]G{ 5hzk]_oq_1s{TemYfAm* 5ijّY固X	c:HN Y%41ɚˈ^O׾{VtN^ =Gi vMͭ-k`$LB9W m~ڸ6 5eVy]+,}k@DHFZ_zt~Gk& x׶ŮȭZmB 5kcK>hu1YtBMl6ְWuT|[_F =`lJwEqj 5jxF;>B^']\qX>&<`     Verdana .Sacdefilmnoqrstuw   x5 
 Cc@ ;шr`<)@& `tb4AL `n,.טn G` (X] Nȶ `z@31oH -z@>1ݑl0av 0,. o?xS= l3 b; 	sh b;  "L3av 0.)\w3AyvE.& 0=  pc1 ``].)^& 9xS= l3t2 "LIɀl0/1 uفt `z@31ܘvF#3  `z@31oH  0:1F$xS #H ` 0 ;>u90 "Le 0= `]  "NL;ay `fc.ߖ-z@>1ݑl шvE1Nu#AqJl0,.ݑ`  fc. n>^b4l+pcG` 06nȶF#L 0-1vavvE0 "BFP ɲ 0/1O
f#vE) X]1L ;Zb0.W& pc  K;$`pc1 Hf; z@,.ސ `xS= l3 `pcv" fc.K 0B- 	1^b4l+pc)FQ#,It `n>1H R vLX] @& z@;"O
g0 0  ]   qR f8 >   	?.@ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ _ ?    _ ; @ TtsPf@  ; < = > ? @ A B G N S Z [ \ ] ^ _ ?K     virtual2_attempts                 virtual   gotoAndPlay R 
   virtual_two   ì g6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
         +     @-Wag          @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(         g     @-gg          @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}          m     @-uYg % H &   ' =F  ( @ORwP ) ;  *  K    hP   
 fS;b2 bnS)x5 ܧXQ',     @'U     b8H 	 f  ͦ@    0! -  @ k(" *   %    E     ==H۴6  -    DU`     VĮݫIF3zN  a    EmX     or3X~3$r6Uy5Zv<f	AN@I/R!39?#$ @"F2>Ca>DP` 	l   3 ?     h 9 ,*@ @ 	 i @  @ @ 	 @ @  9 -"  fp@  9 -G  p@  9 -w*  @@  9 -  @  9 -򪐉  RX@  9 1 J  RP@  9 13
 h ]@  9 1Fʤ@  9 1s	  \@  9 1
  D@  9 1J  Є@  9 1ʤ  $@  9 5  @  9 5  \@  9 5*©  $ @  9 5?  !$ @  9 5Sb  1$@  9 5]©   @  9 5g@  9 5~©  1 @  9 5  A& @  9 5  % @ @ 	 i @  @ @ 	 @ @ 	 i @  @ @ 	 @ @ 	 i @  @ @ 	 @ @ 	 i @  @ F h =t    @  @ d@  @ 
@  @ eD@  @ c:@ F h H    @  @ 
ڐ@  @ 
S@ ?     @ w@   o   p W? 
   fNm0 fc.UttX]L ٠^b   oz@31@`]<) `]<)Gg&, fc.   vE.۲-<) pc!L81ul    b;90u  `] d[#tz@ t2   n\RV  ` 0      r` l+ 0=    \R.ۥdZ pc1#( 	   < ?         @ P        ` @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ?#             _parent   play R   @D؎  h q6! h 4Kү    " f G4*@      6#  á gvirtual F 2 @ TtsPgI *  @ @ @ @ @ F ?    F ; @ TtsPl@              ! " # F I ?!     pentax   FreeToRotate O  ?   vö h#H  @ Pmzh#H  | !@ }  ~  	     ?     shutter_tripped   

   activated  V     . W  3 h    regMark  =   @
@   & b }Z0 element 0 e 6lMU 2 k 
:rІ6 l  7 m /   &8 o n    &: q Ht = r  @ @ @ @ ?       @       uR`mpentax   B @ #  F  theKey Key getCode RIGHT UP this _rotation LEFT DOWN PGUP PGDN HOME            R<    NIL     k   IL     +   IL      NI *      A N	 ?# 8    NIL     m   IL     -   IL      NI *      A N	 ?G#      	NI &      A N    # p     
NI &      A N    G# 1     NI       A        #  L    shutter_tripped snap2 _parent gotoAndPlay element pressingRotate point x  y localToGlobal deltaX _xmouse deltaY _ymouse rotationRadian Math atan2 rotationAngle this _rotation SetupTheElement n t    I  	     R        R            "	 	   "    C      
R  N  N  N  	N       R 	 !?(-DT     	 !	@-DT  O  N     R           NO           NO   D    E   @ A@F   @ PH        x D :  
 f=Hv.oH ( 싄[ L ٠^b vqJn0.kl00.Hf:  `vE.aL `z@31@F#-tz@0.H P  o~[,.vvEv^b nȷd[$2 I   @'\    pMW 
  	 f |Mfwrnn bf|Mn bpbw bntn bwnl bfww劒 J    @'U     b8H 	 f  &@ K  0L -  @ k(h    M  ì m6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
         g R    @-Wam          @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(         m Y    @-gm          @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}          s ^    @-uYme % Hf &  g ' =F h ( @ORwPi ) ; j 2 @ TtsPm@ @ @ @ j ?    j ; @ TtsPq@ ?a   7  virtual2_attempts snapshot_rotation pentax _rotation        G  N s 
   snap2 @       D E F H I J K L M R Y ^ e f g h i j ?  r( snapshot_rotation SetupSnapShotElement snapshot_sigmaN snapshot_sigmaT found_green_arrow Math abs snapshot_blue formatDecimals snapshot_green snapshot_red snapshot_tauNT txtReadings <FONT COLOR="#FFFFFF"><U>Measurements</U></FONT>

Camera angle =  camera_txtTheta  

<U>Arrow Magnitudes</U> 
  Blue arrow  =  
  Green arrow =  
  Blue arrows 
    (greater value) =  
    (lesser value) =  
  Red arrows  =  NeedToTryAgain tolerance virtual2_attempts txtComment That was a good try; however, you should be able to find a larger value for the red arrows.  Please go back to the previous scene and try again.

<FONT COLOR="#99CCCC">Hint:  The angle should be about +11.</FONT> OK...you're getting closer, but you still haven't quite found the largest red arrow value.  Please try just one more time.

<FONT COLOR="#99CCCC">Same hint:  The angle should be near +11.</FONT> Success!  You've done a good job of finding the largest magnitude for the arrows. Although you didn't quite find the largest red arrow magnitude, let's continue.   The largest red arrow value is found at a camera orientation of +11.31. <FONT COLOR="#FFFFFF"><U>Measurements</U></FONT>

Camera angle = +11.31 polaroid gotoAndPlay 

The term for the state of stress you have just discovered is the  <FONT COLOR="#FFFFFF">maximum in-plane shear stress.</FONT>   Just as the term implies, this shear stress is the largest shear stress that exists at any orientation.   

In our snapshot, we note that there are blue arrows and red arrows acting on the surfaces of the element.   We can also note that both blue arrows have the same magnitude (or close to the same magnitude).         =  	         H             R      RH e 	         R     R	 	        R     R ` 	         R     R	 	        R     R	 
        R     R G G  G  I 1   G G  G 	G ;   G  G G  G 	G  G 
G   	 (S@\     R H      	 e@Gz     R H      	 &@QG     R H      	 SY@p=
G     R H      IL       H    |  IL       I    F   I    '   G    &Q      =  	         R     R	 	        R     R    G  G  G G  G 	G  G 
G       ! "R   I K   #G  $G  %G  &G  'G    6  f9|S spolaroid 	    wp@3 f         txtReadings <P ALIGN="LEFT"><FONT FACE="Verdana" SIZE="14" COLOR="#FFCC66">Try to find the camera angle that reveals the largest and the smallest values for the blue and green arrows.</FONT></P> ;   @'
 	>    ' 3  f         txtComment <P ALIGN="LEFT"></P> <   @ \    pK 
  
 fS;b2 bnS)x5 ܧXQ', wnS$/tRH =    @'U     b8H 	 f  Φ@ >  0? -  @ k(@  ì s6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
         m E    @-Was          @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(         s L    @-gs         @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}           NeedToTryAgain   I    Q    @-uYsX % HY &  Z ' =F [ ( @ORwP\ ) ; ] 2 @ TtsPs@ @ @ @ ?   :  polaroid element dynSigmaX _rotation dynSigmaY dynTauXY    N N           N NO   N N           N NO   N N           N NO @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ ] ?    ] ; @ TtsP@  ; < = > @ E L Q X Y Z [ \ ] ?/  q 
 snapshot_rotation SetupSnapShotElement fin polaroid gotoAndStop element dynSigmaX _rotation dynSigmaY dynTauXY       =	     R  N N          N NO  N N          N NO  N 	N          N NO    6  f9|S polaroid \    pLj	 
  
 fI;\bkؚԒfT@,ZMp bnS)x5 ܧXQ', ?    @'U     b8H 	 f  &@ @  0A -  @ k(B  ì 6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
         s G    @-Wa          @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(          N    @-g          @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}           S    @-uYZ % H[ &  \ ' =F ] ( @ORwP^ ) ; _ 2 @ TtsP@  ź,9Ct @ ?   :  polaroid element dynSigmaX _rotation dynSigmaY dynTauXY    N N           N NO   N N           N NO   N N           N NO  ŧ9#U @  Ŕx96 @  łL*9@@  o9@  ]
9ـY    p+ 
 
 Pcv٠X]1 `8_.d[APpc  
K  ;   @/
 @  Jj<9ϲ@  7̛9ے@  %,9|@  O9r^ @   9R?    p50 
 ,c@ %3t `\R.ۥdZ vENw `r`81Gg&, fc.Gd[av`]<)  o+xS31KdXLvE.
`vb;0.l r`7J Hf; vENw `r`81	`"31Nȶ `] PK-t(`] Ld[tav` 0<)ȶLxS  (r`.)Wwd[y$e 0 .pavz@@Hf; 􀀉90 Ld[Atz@,.ސ&L `n^b4GfӲ-t 0-1!91H$e <   @ L@ @ @ @ @ @ @ @ @ @ @ @ ?    b 7 ܨ@ b ?    @ @ @ @ @     xE8 
 Ec@ & r`>1ȶav`l0@Hf; 0@Do
`ɀ `xS31KdXLvE.
` `z@31@F#-\R LvE.
` o?tb6nv  `L4&vE "NLdZLe 081ܘ d[y `X]"ݑnL)0$e 0 vqJpc-Nȷ3 b; v >xS4upc
`ɀ 0= ovvEvP]v@L`],.ݑ`3xS<)
g 2 	8db0.dZe 0= d[  $F  , 0-1@vEJm  `]<) `pc1 L8 `] ۃt 090 n8n,.mCP `xS31KdXLvE.
a#( fc;(X] 
g-txS Ei 00.Hf; `>z@0.
f `r`;"W&tш`]<)&8 `Zb>1ސ  h0= dXqJxS0.3t `pc0m҅a z@;"O
g0	=4 t `z@31@2P 07JlG;A ^b0.: h0;"KWAɀ 090a `b;90Ȱtawh07JҀ m
xS31KdXLvE.
`b;,.0 =  4@ @ @ @ @ @ ?    b 7 ܨ@ b ?    @ @ @ @ @ +   x5B  
 @c@ & `] 2ɀ`];"K@A ``]A.d[APpc  L;8 `z@31@3xS<)O
``db4al `o<n0.o
g;-t 043t `]nu l `^b4l+pc)G& z@ a fc.W&tш``]= @ BxS= ȸEɀv 0=  `]<)3av`] p 0:1FБ  ` 06^#L`db81Nȷ0q `] w3  `]  X]Dnȶɀv 0=  z@0.L#LvE.
`A ` ]   qR f8 >   	?r @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ _ ?    _ ; @ TtsP@  ; < = > ? @ A B G N S Z [ \ ] ^ _ ?s    rotationRadian rotationDegrees thetaRad deltaSigma sigmaX sigmaY center cos2Theta Math cos sin2Theta sin sigmaN tauxy sin2theta sigmaT tauNT cos2theta photo element tauXY gotoAndPlay _rotation , SetupPhotoElement  photo rotationDegrees }  	 !	@-DT    <          <      <  G    <	         	R<	 
        R<   G  G<	     <            G<  N O  N O  N O        N R  N O > ?    polaroid_xy SetupPhotoElement fin gotoAndStop element dynSigmaX _rotation dynSigmaY dynTauXY polaroid_principal polaroid_max_shear               =	      R   N N           N NO   N N           N NO   N N           N NO 'LHz	    =	    	 R 	 N N         	 N NO 	 N N         	 N NO 	 N N         	 N NO &Q
    =	    
 R 
 N N         
 N NO 
 N N         
 N NO 
 N N         
 N NO    6   9Q polaroid_xy < h v𤪳(    3` $   6=   9TSpolaroid_principal x h v𤪳    3` $   6y   9V polaroid_max_shear  h v𤪳$    3` 2    h$P   	 fjj|MvM     @'U     b8H 	 f  Ϧ@   0 -  @ k(  ì 6    )    @)x  @ n@  ^   C^9)k<     @JKW    x|34  
B    n834  
B      A134  
B     @'[@
         @JKW     0     @)x34  
B   @ n@34  
B     @ A0P34  
B     @'[@
              @-Wa          @)0   ?x    ?i    @)034  
B    ?x 34  
B    b@'u(    ?i     0    b@'u(              @-g          @)0   @ PP  @ P  C^9-*     @JJA    @)034  
B    @ PP34  
B    @ P34  
B "    @'}        @JJA     0   Z34  
B #    @'}               @-uY % H &   ' =F  ( @ORwP ) ;  2 @ TtsP@ @ ?   c  polaroid_xy element dynSigmaX _rotation dynSigmaY dynTauXY polaroid_principal polaroid_max_shear    N N           N NO   N N           N NO   N N           N NO  N N          N NO  N N          N NO  N N          N NO  N N          N NO  N N          N NO  N N          N NO @ @ @ @ =    hP 	 yǂ>v.0 `i=]1Sh`0    @/
 @ @ @ @ @     pN7 v 	   4HrvwnXlR RXp^ Rxf`Xvw Rxzmvw`xx`x RhRp Rzmf` R RXp^ R R^hRvw`\zmhRrpx R  0\Xp RZ` R^`zm`vwnhRp`^ RZ Rxrn` Rn`Xpx Rbervw RX R\rntrp`pzmW    @ L@ < v𤪓(    3n@ 	<     3mT@ 	<     3l @ 	<     3j@ 	<     3iT@ M    h 	     xzmvw`xx`x RhRp Rs R^hRvw`\zmhRrp ;  A< v𤪳(    @f @ @ @ @ @ @ ?     7 ܨ@  ?    @ @ @ @ @    p l v$H 	   32zm RrvwhR`pzmXzmhRrpx Rrzmf`vw RzmfXp Rzmf` R RXp^ R R^hRvw`\zmhRrpxW R  2zmf`vw` RXvw` R^hRbebe`vw`pzm R\rnZhRpXzmhRrpx Rrbe RprvwnXlR Rxzmvw`xx D  5.Xp^ Rxf`Xvw Rxzmvw`xxW R RRf` R RXp^ R Rxzmvw`xx`x R^rpPzm R  W*\fXpd` R RrplR Rr|vw Rvw`be`vw`p\` RbevwXn` R\fXpd`xW    @ E@ x v𤪓    3n@ 	x     3mT@ 	x     3l @ 	x     3j@ 	x     3iT@ @    hrW  	     QB
TXؤKw'Gx?8 w  BKx v𤪳    @f @ @ @ @ @ @ ?     7 ܨ @  ?    @ @ @ @ @    pKr$8 	   +@p Rrp` RtXvwzmhR\|lRXvw RrvwhR`pzmXzmhRrpW R` RbehRp^ Rzmf` R  -lRXvwd`xzm RprvwnXlR Rxzmvw`xx`xW R RRf`x` Rxzmvw`xx`x RXvw` R  5\XlRlR`^ RtvwhRp\hRtXlR Rxzmvw`xx`xW R RJp RtvwhRp\hRtXlR Rxzmvw`xx A  W!tlRXp`xW Rzmf`vw` RhRx Rpr Rxf`Xvw Rxzmvw`xxW    @ @@ @ @ @ @ @ ?     7 ܨ@  ?    @ @ @ @ @    p r-H 	   $@p RXprzmf`vw RrvwhR`pzmXzmhRrpW R` RbehRp^ Rzmf` RnXhRn|n R  xf`Xvw Rxzmvw`xxW R RRfhRx RrvwhR`pzmXzmhRrp RhRx R  RXX R  5+bevwrn Rzmf` RtvwhRp\hRtXlR Rxzmvw`xx RrvwhR`pzmXzmhRrpW R R@p R  W-d`p`vwXlRW RZrzmf RprvwnXlR Rxzmvw`xx RXp^ Rxf`Xvw Rxzmvw`xx R  y'X\zm Rrp Rzmf` RnXhRn|n Rxf`Xvw Rxzmvw`xx RtlRXp`xW    @ s @  v𤪓#    3n@ 	     3mT@ 	     3l @ 	     3j@ 	     3iT@  ?    E    hHz 	     nXhRn|n Rxf`Xvw Rxzmvw`xx   C~ v𤪳$    @f  ; @ TtsP@  ; < = w x y                     ?N     myDate Date txtDate toString           @           R 
   final_scene ?    polaroid_xy SetupPhotoElement fin gotoAndStop element dynSigmaX _rotation dynSigmaY dynTauXY polaroid_principal polaroid_max_shear               =	      R   N N           N NO   N N           N NO   N N           N NO 'LHz	    =	    	 R 	 N N         	 N NO 	 N N         	 N NO 	 N N         	 N NO &Q
    =	    
 R 
 N N         
 N NO 
 N N         
 N NO 
 N N         
 N NO  h 0*U     ? "    X` 	      fvB_  *    ]_]([  33 f f5t Zn`|8V "    X` 	  33  fvB_  $    \`]_  33    5kZ}!Lt/
 {     S %      e@ 
5`      e@ 
5`      e@ 
5`   %         printasbitmap:  _level0       ) @  +    a.p"  	 333pbvMvMtnl     @'U  -  @ k(h    J    hP  
  f LfK3 pc NȰ"ɀvEC    &@ `	%    w
(  f          txtName 	   %@LN	4    xĘ  0  333         txtDate 12 pt Verdana 
  @ A    6   9Q polaroid_xy F h v𤪳(    ? $   6G   9TSpolaroid_principal  h v𤪳    ? $   6   9V polaroid_max_shear  h v𤪳$    ?    p-p 
    *Jw1W&`]@Hf; 04;  `vE.m" pcm҅2db 
 o(xS= l3 X]JNȵ X]  Uۃ `]0.Hf; `pc Nȷ: (z+xS= l3t 04Ll04FP I~h0<):dbB-0`]/1  A(z@90 W&l[ vqJpc k z@4r z@;"O
g3L (n(4v  07JoHӲ-l0 d\" h0= &-pc oH$e  	c a0 @E.Ř` q)(] f81t4"c. yL 
 0,.ݑlL^b 
 m
)z@90 W&tшz@0.
g-txS0.  pc-Ld[Atz@,.ސ&H (   *Bl81ܘ& `xS= l3t 0,.ސ шh081ސ   0<) `pc
 >&z@@D &- r`21ua h0;"KWAɀxS 
g:╙ `X])Hf;l) 0A.:  0/1ȶ `r`81I($ 0.)Vnpɀ(tb>1ސ  *xS= oHɀv 0<)ȶL `X]  Hf:  `xS,.ۥɀ`pc  8avǄ[ 
 ~)r`= dXɀh00.Hpc@ i X]1ɀ `\R0
ft   k+X] F#Lh0-1``]81ސAɀxS L t`];"ۥ; fc. )l0,.ݑlF  `xS= l3t 0,.ސ 3t `tb90w *0 `Zb90p  #tb;"u+Aшl0 Hd[L`]<): fc.҅(|cJ  jxS31KdXLvE.
` z@0.    @/2
 	2    g*
P0   f         txtIdentifier 1999999    @ F v𤪓(    ?@ ?   c  polaroid_xy element dynSigmaX _rotation dynSigmaY dynTauXY polaroid_principal polaroid_max_shear    N N           N NO   N N           N NO   N N           N NO  N N          N NO  N N          N NO  N N          N NO  N N          N NO  N N          N NO  N N          N NO 	F     ?T@ 	F     ? @ 	F     ?@ 	F     ?T@ M    h 	   f   xzmvw`xx`x RhRp Rs R^hRvw`\zmhRrp E  AF v𤪳(    @  v𤪓@  v𤪓    ?h@  v𤪳    ?@  v𤪳    ?4@ 	     ?@ @    hrW  	   f   QB
TXؤKw'Gx?8   BK v𤪳    @ @  v𤪓#    ?@ 	     ?T@ 	     ? @ 	     ?@ 	     ?T@ E    hHz 	   f   nXhRn|n Rxf`Xvw Rxzmvw`xx   C~ v𤪳$    @ @ 
   #P ?    @   