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Consider two transformations:
\(T_1\): A reflection in the line \(y = x\sqrt{3}\).
\(T_2\): An enlargement centered at the origin with scale factor 2.
Find the matrix \(\mathbf{A}\) representing \(T_1\). (Recall: \(\tan(60^\circ)=\sqrt{3}\)).
Find the matrix \(\mathbf{B}\) representing \(T_2\).
Find the matrix \(\mathbf{C}\) representing the composite transformation \(T_1\) followed by \(T_2\).
Find the image of the point \(Q(2, 0)\) under this composite transformation.
Find the coordinates of point \(R\) such that its image under this composite transformation is \(R'(2, 2\sqrt{3})\).
(You are given that \(\mathbf{C}^{-1} = \begin{pmatrix} -0.25 & \frac{\sqrt{3}}{4} \\ \frac{\sqrt{3}}{4} & 0.25 \end{pmatrix}\)).
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