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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.
  1. Find the matrix \(\mathbf{A}\) representing \(T_1\). (Recall: \(\tan(60^\circ)=\sqrt{3}\)).
  2. Find the matrix \(\mathbf{B}\) representing \(T_2\).
  3. Find the matrix \(\mathbf{C}\) representing the composite transformation \(T_1\) followed by \(T_2\).
  4. Find the image of the point \(Q(2, 0)\) under this composite transformation.
  5. 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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