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

Thu May 4 16:40:05 2006 UTC (7 years, 1 month ago) by jjholt
File size: 1435 byte(s)
```Added tags.  --JH
```

```    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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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
```

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