The matrix M is given by \(\mathbf{M} = \begin{pmatrix} \frac{1}{2} & -\frac{1}{2}\sqrt{3} & \begin{pmatrix} 14 & 0 \\ 0 & 1 \end{pmatrix} \\ \frac{1}{2}\sqrt{3} & \frac{1}{2} & \end{pmatrix}\).

1. The matrix M represents a sequence of two geometrical transformations in the x-y plane. Give full details of each transformation, and make clear the order in which they are applied.
2. Write \(\mathbf{M}^{-1}\) as the product of two matrices, neither of which is I.
3. Find the equations of the invariant lines, through the origin, of the transformation represented by M.
4. The triangle ABC in the x-y plane is transformed by M onto triangle DEF. Given that the area of triangle DEF is 28 cm², find the area of triangle ABC.