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We present stellar rotation curves and velocity dispersion profiles for 104 quiescent galaxies at $z=0.6-1$ from the Large Early Galaxy Astrophysics Census (LEGA-C) spectroscopic survey. Rotation is typically probed across 10-20kpc, or to an average of 2.7${\rm R_e}$. Combined with central stellar velocity dispersions ($\sigma_0$) this provides the first determination of the dynamical state of a sample selected by a lack of star formation activity at large lookback time. The most massive galaxies ($M_{\star}>2\times10^{11}\,M_{\odot}$) generally show no or little rotation measured at 5kpc ($|V_5|/\sigma_0, Comment: 30 pages, 18 figures, Accepted for Publication in ApJ

Using high-resolution spectra from the VLT Large Early Galaxy Astrophysics Census (LEGA-C) program, we reconstruct the star formation histories (SFHs) of 607 galaxies at redshifts z - 0.6-1.0 and stellar masses. greater than or similar to 10(10) M circle dot using a custom full spectrum fitting algorithm that incorporates the emcee and FSPS packages. We show that the mass-weighted age of a galaxy correlates strongly with stellar velocity dispersion (sigma(*)) and ongoing star formation (SF) activity, with the stellar content in higher-sigma(*) galaxies having formed earlier and faster. The SFHs of quiescent galaxies are generally consistent with passive evolution since their main SF epoch, but a minority show clear evidence of a rejuvenation event in their recent past. The mean age of stars in galaxies that are star-forming is generally significantly younger, with SF peaking after z < 1.5 for almost all star-forming galaxies in the sample: many of these still have either constant or rising SFRs on timescales > 100 Myr. This indicates that z > 2 progenitors of z similar to 1 star-forming galaxies are generally far less massive. Finally, despite considerable variance in the individual SFHs, we show that the current SF activity of massive galaxies (>L-*) at z similar to 1 correlates with SF levels at least 3 Gyr prior: SFHs retain "memory" on a large fraction of the Hubble time. Our results illustrate a novel approach to resolve the formation phase of galaxies, and, by identifying their individual evolutionary paths, one can connect progenitors and descendants across cosmic time. This is uniquely enabled by the high-quality continuum spectroscopy provided by the LEGA-C survey.