Consider a thin square plate on the z = 0 plane with mass density given byo(x, y) = C ((x - 1)²y² + x¹y²),(4)and whose total mass is M. The plate has a side length of two meters, and its center lies atthe origin. The infinitesimal mass element is given by:dM = o(x, y)dxdy(5)1. What are the units of C? Find an expression for C in terms of M.2. Find the coordinates of the center of mass XCM.3. Find the moment of inertia around the z-axis:1-L LI=r²o(x, y)dxdy(6)You may leave your final answer as the sum of two fractions.4. Now find the moment of inertia along the (x = 2, y = 0) axis.

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Consider a thin square plate on the z = 0 plane with mass density given by o(x, y) = C ((x - 1)²y² + x¹y²), and whose total mass is M. The plate has a side length of two meters, and its center lies at the origin. The infinitesimal mass element is given by: dM = 0 o(x, y) dxdy