A proton moves in the \(x, y\) plane with velocity \(v=(3 / 5) c\), at an angle of \(45^{\circ}\) to both the \(x\) and \(y\) axes. (a) Find all four components of the proton's four-vector velocity \(v^{\mu}\) and evaluate the invariant square of its components \(\eta_{\mu u} u^{\mu} v^{u}\). (b) Find all four components of the proton's four-vector velocity in a frame moving in the positive \(x\) direction at velocity \(V=(4 / 5) c\). (c) Evaluate explicitly the invariant square of its components in this frame.