The matrix M is given by \(M = \begin{pmatrix} \frac{1}{2}\sqrt{2} & -\frac{1}{2}\sqrt{2} \\ \frac{1}{2} & \frac{1}{2}\sqrt{2} \end{pmatrix} \begin{pmatrix} 1 & k \\ 0 & 1 \end{pmatrix}\), where \(k\) is a constant.

(a) The matrix M represents a sequence of two geometrical transformations. State the type of each transformation, and make clear the order in which they are applied.

(b) The triangle ABC in the \(x-y\) plane is transformed by M onto triangle DEF. Find, in terms of \(k\), the single matrix which transforms triangle DEF onto triangle ABC.

(c) Find the set of values of \(k\) for which the transformation represented by M has no invariant lines through the origin.