In the framework of dipole approximation, it is shown that the oscillator strengths of transitions as well as the dipole moments for transitions for one-particle electron quantum-confined states emerging above the spherical surface quantum dot of aluminum oxide assume giant values considerably (by two orders of magnitude) exceeding the typical values of the corresponding quantities for dielectrics. It has been established that the giant values of the light absorption cross section in the nanosystems under investigation make it possible to use such nanosystems as strongly absorbing nanomaterials in a wide range of infrared waves with a wavelength that can be varied in a wide range depending in the type of contacting materials.