1. If a moving point $P(x, y)$ rotates counterclockwise on the unit circle with a constant angular velocity $\omega$, then the motion of point $Q\left(-2 x y, y^{2}-x^{2}\right)$ is
A. rotating clockwise on the unit circle with angular velocity $\omega$
B. rotating counterclockwise on the unit circle with angular velocity $\omega$
C. rotating clockwise on the unit circle with angular velocity $2 \omega$
D. rotating counterclockwise on the unit circle with angular velocity $2 \omega$
1. C Hint: Let $x=\cos \omega t, y=\sin \omega t$ then $-2 x y=-\sin 2 \omega t=\cos \left(\frac{3}{2} \pi-2 \omega t\right), y^{2}-x^{2}=$ $-\cos 2 \omega t=\sin \left(\frac{3}{2} \pi-2 \omega t\right)$