4
QuizMultiple Choice

Vector Multiplication Using Matrices — Quiz

Question 4 • Precalculus

Which transformation matrix would result in a 300 degrees counterclockwise rotation about the origin?

Answer
A
the 2 by 2 matrix, row 1, column 1, 1 half column 2, the fraction with numerator square root of 3 and denominator 2 row 2, column 1, negative the fraction with numerator square root of 3 and denominator 2 column 2, 1 half
B
the 2 by 2 matrix, row 1, column 1, negative 1 half column 2, the fraction with numerator square root of 3 and denominator 2 row 2, column 1, negative the fraction with numerator square root of 3 and denominator 2 column 2, negative 1 half
C
the 2 by 2 matrix, row 1, column 1, negative the fraction with numerator square root of 3 and denominator 2 column 2, negative 1 half row 2, column 1, 1 half column 2, negative the fraction with numerator square root of 3 and denominator 2
D
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

Explanation

A counterclockwise rotation by θ uses the matrix [[cos θ, −sin θ], [sin θ, cos θ]]. For 300°, cos 300° = 1/2 and sin 300° = −√3/2, giving [[1/2, √3/2], [−√3/2, 1/2]]. This matches choice A.

AI-written and checked against the verified answer.

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