What matrix represents an anticlockwise rotation by 90 degrees (pi/2 radians) about the origin in R^2?
Answer and explanation
Correct answer: A. [[0, -1], [1, 0]]
- Step 1: Rotation matrix: R(theta) = [[cos theta, -sin theta], [sin theta, cos theta]]. Step 2. For theta = pi/2: cos(pi/2) = 0, sin(pi/2) = 1. Matrix is [[0, -1], [1, 0]]. Answer: [[0, -1], [1, 0]]. Why not the others: Applying to (1, 0) yields (0, 1), confirming a 90-degree anticlockwise turn.
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