BTW: The (usually hidden by default) OriginX, OriginY and OriginZ dials move the centre of rotation and scaling:

In this example the cone is on x=0.0, y=0.0, z = 0.0 in universe coordinates. I moved the origin of the sphere 1.0 m (-0.381 PNU) in the positive x-direction and rotated the sphere around the Y-axis through that new origin by 63 degrees. As you can see it is moved off the z=0.0 line (the edge loop betwee the centre of the base of the cone and the green cross).