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Rotate!!!

Source: 1984 National High School Mathematics League, Exam One, Problem 7

February 22, 2020

Problem Statement

A moving point P(x,y)P(x,y) rotate anticlockwise around unit circle, who seangular speed is ω\omega. Then how does Q(−2xy,y2−x2)Q(-2xy,y^2-x^2) moves? (A)\text{(A)} Rotate clockwise around unit circle, who seangular speed is ω\omega. (B)\text{(B)} Rotate anticlockwise around unit circle, who seangular speed is ω\omega. (C)\text{(C)} Rotate clockwise around unit circle, who seangular speed is 2ω2\omega. (D)\text{(D)} Rotate anticlockwise around unit circle, who seangular speed is 2ω2\omega.
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