  We study the structure and total energy of a strange quark star (SQS) endowed
with a strong magnetic field with different rotational frequencies. The MIT bag
model is used, with the density-dependent bag constant for the equation of
state (EOS). The EOS is computed considering the Landau quantization effect
regarding the strong magnetic fields (up to $5\times10^{17}$ G) in the interior
of the strange quark star. Using the LORENE library, we calculate the
structural parameters of SQS for different setups of magnetic field strengths
and rotational frequencies. In each setup, we perform calculations for $51$
stellar configurations, with specified central enthalpy values. We investigate
the configurations with the maximum gravitational mass of SQS in each setup.
Our models of SQSs are compared in the maximum gravitational mass, binding
energy, compactness, and deformation of the star. We show that the
gravitational mass might exceed $2.3 M_\odot$ in some models, which is
comparable with the mass of the recently detected ``black widow'' pulsar
\emph{PSR J0952-0607} and the mass of \emph{GW190814} detected by the
LIGO/Virgo collaboration. The deformation and maximum gravitational mass of SQS
can be characterized by simple functions that have been fitted to account for
variations in both magnetic field strength and frequency. Rapidly rotating
strange stars have a minimum gravitational mass given by the equatorial
mass-shedding limit.
