Consider the following maps of polynomials \(S:\mathcal{P}\rightarrow\mathcal{P}\) and \(T:\mathcal{P}\rightarrow\mathcal{P}\) defined by

\[ S(h(x))= 2 \, x - 5 \, h'\left(x\right) \hspace{1em} \text{and} \hspace{1em} T(h(x))= 5 \, x^{3} h\left(x\right) + h\left(x\right) \]

Explain why one these maps is a linear transformation and why the other map is not.