[填空题]
A geometric transformationa0*akxq 5 d0nb T (1,kxucu6q-xqu/ r gjc8tiq.: $\left(\begin{array}{l}x \\ y\end{array}\right) \mapsto\left(\begin{array}{c}x \\ y^{\prime}\end{array}\right)$ is defined by
$\left(\begin{array}{l}
x^{\prime} \\
y^{\prime}
\end{array}\right)=\left(\begin{array}{cc}
\cos \left(\frac{\pi}{3}\right) & \sin \left(\frac{\pi}{3}\right) \\
\sin \left(\frac{\pi}{3}\right) & \cos \left(\frac{\pi}{3}\right)
\end{array}\right)\left(\begin{array}{l}
x \\
y
\end{array}\right)-\frac{\sqrt{3}}{2}\left(\begin{array}{l}
1 \\
2
\end{array}\right)$ .
1. Find the coordinates of the image of the point $P(1,-\sqrt{3})$ . $\left(-a-\frac{\sqrt{b}}{c},-\sqrt{d}\right) $ a = b = c = d =
2. Given that T : $\left(\begin{array}{l}a \\ b\end{array}\right) \mapsto \frac{1}{2}\left(\begin{array}{l}a \\ b\end{array}\right)$ , find the value of a and the value of b . a = b =
A rhombus R with vertices lying on the x y -plane is transformed by T .
3. Show that the area of the image is half the size of R .
