  We report on the submillimeter properties of Sagittarius A* derived from
observations with the Submillimeter Array and its polarimeter. We find that the
spectrum of Sgr A* between 230 and 690 GHz is slightly decreasing when measured
simultaneously, indicating a transition to optically thin emission around
300-400 GHz. We also present very sensitive and well calibrated measurements of
the polarization of Sgr A* at 230 and 345 GHz. With these data we are able to
show for the first time that the polarization of Sgr A* varies on hour
timescales, as has been observed for the total intensity. On one night we find
variability that may arise from a polarized "blob" orbiting the black hole.
Finally, we use the ensemble of observations to determine the rotation measure.
This represents the first statistically significant rotation measure
determination and the only one made without resorting to comparing position
angles measured at separate epochs. We find a rotation measure of
(-5.6+/-0.7)x10^5 rad/m^2, with no evidence for variability on inter-day
timescales at the level of the measurement error. The stability constrains
interday fluctuations in the accretion rate to 8%. The mean intrinsic
polarization position angle is 167+/-7 degrees and we detect variations of
31+18/-9 degrees. This separation of intrinsic polarization changes and
possible rotation measure fluctuations is now possible because of the frequency
coverage and sensitivity of our data. The observable rotation measure restricts
the accretion rate to the range 2x10^{-7} Msun/yr to 2x10^{-9} Msun/yr, if the
magnetic field is near equipartition and ordered.
