View of /trunk/NationalProblemLibrary/Rochester/setLinearAlgebra14TransfOfRn/ur_la_14_15.pg

    1 ## DESCRIPTION
    2 ## Linear Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS ('linear algebra','vector space','linear transformation')
    6 ## Tagged by cmd6a 5/3/06
    7 
    8 ## DBsubject('Linear Algebra')
    9 ## DBchapter('Vector Spaces')
   10 ## DBsection('Linear Transformations')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGgraphmacros.pl",
   28 "PGmatrixmacros.pl",
   29 "PGnumericalmacros.pl",
   30 "PGauxiliaryFunctions.pl"
   31 );
   32 
   33 TEXT(beginproblem());
   34 $showPartialCorrectAnswers = 1;
   35 
   36 @dir = ("counterclockwise", "clockwise");
   37 $dir_tag = random(0,1,1);
   38 
   39 @angle = (30, 45, 60, 120, 135, 150);
   40 $angle_tag = random(0,5,1);
   41 $deg = ((-1)**$dir_tag)*$angle[$angle_tag];
   42 
   43 $a = "cos($deg*pi/180)";
   44 $b = "(-1)*sin($deg*pi/180)";
   45 $c = "sin($deg*pi/180)";
   46 $d = "cos($deg*pi/180)";
   47 
   48 BEGIN_TEXT
   49 
   50 Find the matrix \(A\) of the linear transformation \(T\) from \({\mathbb R}^2\) to \({\mathbb R}^2\)
   51 that rotates any vector through an angle of \($angle[$angle_tag] ^\circ \) in the $dir[$dir_tag]
   52 direction.
   53 $BR
   54 \{ mbox([ '\(A=\)', answer_matrix(2,2,10), '.' ]) \}
   55 
   56 END_TEXT
   57 
   58 ANS(fun_cmp($a));
   59 ANS(fun_cmp($b));
   60 ANS(fun_cmp($c));
   61 ANS(fun_cmp($d));
   62 
   63 ENDDOCUMENT();       # This should be the last executable line in the problem.
   64