4. If the moving point $P(x, y)$ rotates counterclockwise on the unit circle with a constant angular velocity $\omega$, then the motion equation of point $Q\left(-2 x y, y^{2}-x^{2}\right)$ is ( ).
(A) rotates clockwise on the unit circle with angular velocity $\omega$
(B) rotates counterclockwise on the unit circle with angular velocity $\omega$
(C) rotates clockwise on the unit circle with angular velocity $2 \omega$
(D) rotates counterclockwise on the unit circle with angular velocity $2 \omega$