The beach ball shown in Figure P12.27 undergoes a rotation of \(90^{\circ}\) around the \(x\) axis and then a rotation of \(90^{\circ}\) around the \(y\) axis. A second, identically colored ball undergoes first the rotation of \(90^{\circ}\) around the \(y\) axis and then the \(90^{\circ}\) rotation around the \(x\) axis. What additional rotations are necessary to put the second ball in exactly the same orientation as the first?

Data from Figure P12.27