  Cosmological applications of the "redshift - angular size" test require
knowledge of the linear size of the "standard rod" used. In this paper, we
study the properties of a large sample of 140 milliarcsecond compact radio
sources with flux densities measured at 6 cm and 20 cm, compiled by Gurvits et
al.(1999). Using the best-fitted cosmological parameters given by Planck/WMAP9
observations, we investigate the characteristic length $l_m$ as well as its
dependence on the source luminosity $L$ and redshift $l_m=l L^\beta (1+z)^n$.
For the full sample, measurements of the angular size $\theta$ provide a tight
constraint on the linear size parameters. We find that cosmological evolution
of the linear size is small ($|n|\simeq 10^{-2}$) and consistent with previous
analysis. However, a substantial evolution of linear sizes with luminosity is
still required ($\beta\simeq 0.17$). Furthermore, similar analysis done on
sub-samples defined by different source optical counterparts and different
redshift ranges, seems to support the scheme of treating radio galaxies and
quasars with distinct strategies. Finally, a cosmological-model-independent
method is discussed to probe the properties of angular size of milliarcsecond
radio quasars. Using the corrected redshift - angular size relation for quasar
sample, we obtained a value of the matter density parameter,
$\Omega_m=0.292^{+0.065}_{-0.090}$, in the spatially flat $\Lambda$CDM
cosmology.

Cosmology and Nongalactic Astrophysics