(a) In a Cartesian coordinate system that has axes \(x\) and \(y\), the coordinates of a certain point \(\mathrm{P}\) are \((x, y)\). What are the coordinates of \(\mathrm{P}\) in a Cartesian coordinate system that has axes \(x^{\prime}\) and \(y^{\prime}\) if the origins coincide but the \(x^{\prime}\) axis is tipped above the \(x\) axis by an angle \(\varphi\) ?

(b) If the \(x\) and \(y\) coordinates of \(\mathrm{P}\) are \((5.0 \mathrm{~m}, 2. 0 \mathrm{~m})\) and \(\varphi=30^{\circ}\), determine \(\left(x^{\prime}, y^{\prime}\right)\).