8
QuizMultiple Choice

Vector Multiplication Using Matrices — Quiz

Question 8 • Precalculus

Which angle of rotation is determined by the matrix shown? the 2 by 2 matrix, row 1, column 1, 1 half column 2, negative the fraction with numerator square root of 3 and denominator 2 row 2, column 1, the fraction with numerator square root of 3 and denominator 2 column 2, 1 half

Answer
A
300 degrees
B
120 degrees
C
30 degrees
D
60 degrees

Explanation

A rotation matrix has the form [[cos θ, −sin θ], [sin θ, cos θ]]. Here, cos θ = 1/2 and sin θ = √3/2, which correspond to θ = 60 degrees. Therefore, the matrix determines a 60-degree rotation.

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