  We study the scaling relations between the luminosities, sizes, and rotation
velocities of disk galaxies in the SFI++, with a focus on the size-luminosity
(RL) and size-rotation velocity (RV) relations. Using isophotal radii instead
of disk scale-lengths as a size indicator, we find relations that are
significantly tighter than previously reported: the correlation coefficients of
the template RL and RV relations are r=0.97 and r=0.85, which rival that of the
more widely studied LV (Tully-Fisher) relation. The scatter in the SFI++ RL
relation is 2.5-4 times smaller than previously reported for various samples,
which we attribute to the reliability of isophotal radii relative to disk
scale-lengths. After carefully accounting for all measurement errors, our
scaling relation error budgets are consistent with a constant intrinsic scatter
in the LV and RV relations for velocity widths logW>2.4, with evidence for
increasing intrinsic scatter below this threshold. The scatter in the RL
relation is consistent with constant intrinsic scatter that is biased by
incompleteness at the low-luminosity end. Possible applications of the
unprecedentedly tight SFI++ RV and RL relations are investigated. Just like the
Tully-Fisher relation, the RV relation can be used as a distance indicator: we
derive distances to galaxies with primary Cepheid distances that are accurate
to 25%, and reverse the problem to measure a Hubble constant H_0=72+/-7
km/s/Mpc. Combining the small intrinsic scatter of our RL relation
(0.034+/-0.001 log(kpc/h)) with a simple model for disk galaxy formation, we
find an upper limit on the range of disk spin parameters that is a factor of ~7
smaller than that of the halo spin parameters predicted by cosmological
simulations. This likely implies that the halos hosting Sc galaxies have a much
narrower distribution of spin parameters than previously thought.
