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Let \(T\) be a linear transformation defined by the matrix \(\mathbf{A} = \begin{pmatrix} 3 & x \\ 1 & 2 \end{pmatrix}\), where \(x\) is a constant.
A parallelogram with area \(5\) cm\(^2\) is transformed by \(T\) into an image with area \(30\) cm\(^2\).
  1. Write down an expression for the determinant of \(\mathbf{A}\) in terms of \(x\).
  2. Find the two possible values of \(x\).
  3. Given that the transformation reverses the orientation of the shape (i.e., the determinant is negative), find the value of \(x\).

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