Answer
a) ${\bf 1.96\;\times 10^3}\;\rm rad/s$
b) ${\bf 70.7}\;\rm V$
Work Step by Step
$$\color{blue}{\bf [a]}$$
We know that $\phi=\omega t$, So
$$\omega=\dfrac{\phi}{t}$$
Plug the given and don't forget to convert the angle to radians.
$$\omega=\dfrac{225^\circ}{2\times 10^{-3}}\times \dfrac{\pi\;\rm rad}{180^\circ }$$
$$\omega=\color{red}{\bf 1.96\;\times 10^3}\;\rm rad/s$$
$$\color{blue}{\bf [b]}$$
We know that the emf is given by
$$\varepsilon=\varepsilon_0\cos(\omega t)$$
So the peak emf is given by
$$\varepsilon_0=\dfrac{\varepsilon}{\cos\phi}$$
Plug the known;
$$\varepsilon_0=\dfrac{-50}{\cos(225^\circ)}$$
$$\varepsilon_0=\color{red}{\bf 70.7}\;\rm V$$
