Consider a square plane lamina with coordinate axes \(x, y\) in the plane with origin at the center of the square and which are perpendicular to edges of the square. If the moment of inertia about each of these two axes is \(I_{0}\), what are the moments of inertia about axes \(x^{\prime}\) and \(y^{\prime}\) in the plane turned about the \(z\) axis by a \(30^{\circ}\) angle relative to the original two axes?