Rotate ellipsoid by holding from one point and centroid will not change

How to take from head coordinate (longest semi axis) of ellipsoid and place it to new coordinate. Centroid will remain pinned. After rotation to new direction all new [x,y,z] coordinates of ellipsoid is needed.

[Sayfallah Ben fraj]

So i been trying to solve the exact same problem by projecting the local orthognal vectors to a gloabl orgthognal vectors unsing Z*X + T where Z is the new set of orthogonal vectors and T is the translation but no luck.

[Meg Noah]

Generally, when you rotate a feature in 2D space or 3D space, first translate the rotation point on the feature to the origin, then apply the rotation, then translate the rotation point on the feature back to its position in space.