7. If the moving point $P(x, y)$ rotates counterclockwise on the unit circle with a constant angular velocity $\omega$, then the motion equation of the 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 $2 \omega$
(C)
7. 【Analysis and Solution】Express the coordinates of the moving point $P(x, y)$ in parametric form.
$$
\left\{\begin{array}{l}
x=\cos \omega t \\
y=\sin \omega t
\end{array},(\omega>0) .\right.
$$

Then $-2 x y=-\sin 2 \omega t=\cos \left(-2 \omega t+\frac{3}{2} \pi\right)$,
$$
y^{2}-x^{2}=-\cos 2 \omega t=\cos \left(-2 \omega t+\frac{2 \pi}{3}\right) \text {. }
$$

Thus, the parametric equations for the trajectory of point $Q\left(-2 x y, y^{2}-x^{2}\right)$ are
$$
\left\{\begin{array}{l}
x^{\prime}=\cos \left(-2 \omega t+\frac{3}{2} \pi\right), \\
y^{\prime}=\sin \left(-2 \omega t+\frac{2 \pi}{3}\right),
\end{array}\right.
$$

It is clear that the rotation directions of $\omega t$ and $-2 \omega t$ are opposite. Point $P(x, y)$ moves counterclockwise on the unit circle, so point $Q$ moves clockwise on the unit circle with an angular velocity of $2 \omega$.