  The behaviour of matrix string theory in the background of a type IIA pp wave
at small string coupling, g_s << 1, is determined by the combination M g_s
where M is a dimensionless parameter proportional to the strength of the
Ramond-Ramond background. For M g_s << 1, the matrix string theory is
conventional; only the degrees of freedom in the Cartan subalgebra contribute,
and the theory reduces to copies of the perturbative string. For M g_s >> 1,
the theory admits degenerate vacua representing fundamental strings blown up
into fuzzy spheres with nonzero lightcone momenta. We determine the spectrum of
small fluctuations around these vacua. Around such a vacuum all N-squared
degrees of freedom are excited with comparable energies. The spectrum of masses
has a spacing which is independent of the radius of the fuzzy sphere, in
agreement with expected behaviour of continuum giant gravitons. Furthermore,
for fuzzy spheres characterized by reducible representations of SU(2) and
vanishing Wilson lines, the boundary conditions on the field are characterized
by a set of continuous angles which shows that generically the blown up strings
do not ``close''.
