10. The transformation \(P\) is an enlargement, centre the origin, with scale factor \(k\), where \(k > 0\) The transformation \(Q\) is a rotation through angle \(\theta\) degrees anticlockwise about the origin. The transformation \(P\) followed by the transformation \(Q\) is represented by the matrix $$\mathbf { M } = \left( \begin{array} { c c } - 4 & - 4 \sqrt { 3 }
4 \sqrt { 3 } & - 4 \end{array} \right)$$

1. Determine
   1. the value of \(k\),
   2. the smallest value of \(\theta\) A square \(S\) has vertices at the points with coordinates \(( 0,0 ) , ( a , - a ) , ( 2 a , 0 )\) and \(( a , a )\) where \(a\) is a constant. The square \(S\) is transformed to the square \(S ^ { \prime }\) by the transformation represented by \(\mathbf { M }\).
2. Determine, in terms of \(a\), the area of \(S ^ { \prime }\)
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