  We find the rules of the conformal transformation for the energetic
quantities such as the Einstein energy-momentum complex, the Bergmann-Thomson
angular momentum complex, the superenergy tensor, and the angular supermomentum
tensor of gravitation and matter. We show that the conformal transformation
rules for the matter parts of both the Einstein complex and the
Bergmann-Thomson complex are fairly simple, while the transformation rules for
their gravitational parts are more complicated. We also find that the
transformational rules of the superenergy tensor of matter and the superenergy
tensor of gravity are quite complicated except for the case of a pure gravity.
In such a special case the superenergy density as well as the sum of the
superenergy density and the matter energy density are invariants of the
conformal transformation. Besides, in that case, a conformal invariant is also
the Bel-Robinson tensor which is a part of the superenergy tensor. As for the
angular supermomentum tensor of gravity - it emerges that its transformational
rule even for a pure gravity is quite complicated but this is not the case for
the angular supermomentum tensor of matter. Having investigated some
technicalities of the conformal transformations, we also find the conformal
transformation rule for the curvature invariants and, in particular, for the
Gauss-Bonnet invariant in a spacetime of arbitrary dimension.
