The "50 km s-1" molecular cloud (M-0.02-0.07) near the Galactic center has been mapped in the CS J = 7-6 and 5-4 rotational transitions. In addition, mid-infrared fine-structure lines of [Ne II], [Ar III], and [S IV] have been observed toward the compact H II regions located near the cloud's core. We find the following: (1) A dense molecular layer, with n approximately 1-2 x 10(6) cm-3, curves around the entire eastern half of the Sgr A East shell source, implying that Sgr A East is impacting upon and compressing this molecular cloud. No corresponding molecular layer is seen on the opposite side of Sgr A East. (2) Just inside of this curved ridge, highly red- and blueshifted gas is seen, which has likely been accelerated by the blast wave. (3) Just to the east of this compressed ridge lies the true molecular cloud core, as well as the string of compact H II regions Sgr A East-A through D. Since the compression wave has not yet reached either the cloud core or the compact H II regions, they must be due to an episode of collapse and star formation which occurred prior to the impact of Sgr A East. (4) The sources exciting the compact H II regions have spectra and luminosities corresponding approximately to O8-O9 stars. These results suggest a two-component model for the dense gas in M-0.02-0.07: a normal, dense, star-forming cloud core, and a compression wave which has advanced into the cloud from the direction of Sgr A East.