(very thin) 1” x 1” square tile is painted purple. The paint mass density increases steadily from one corner to the opposite corner starting at 0 oz./sq. inch and ending with 1 oz./sq. inch. Where is the center of mass of the tile? Suppose the tile is balanced on a pencil passing under the center of mass. Compute the moment of inertia of the tile about an axis along the pencil for any possible such placement of the pencil. Which pencil placement angle maximizes the moment of inertia?