7. 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. 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 $2 \omega$
$$
\left\{\begin{array} { l } 
{ x = \cos \omega t , } \\
{ y = \sin \omega t , }
\end{array} \Rightarrow \left\{\begin{array}{l}
X=-2 x y=-\sin 2 \omega t=\cos \left(\frac{3 \pi}{2}-2 \omega t\right), \\
Y=y^{2}-x^{2}=-\cos 2 \omega t=\sin \left(\frac{3 \pi}{2}-2 \omega t\right),
\end{array}\right.\right.
$$

Thus, point $Q$ moves clockwise on the unit circle with angular velocity $2 \omega$, so the answer is $C$.