We have undertaken a spectral-line imaging survey of a 6 x 6 arcmin^2 area around Sgr B2 near the centre of the Galaxy, in the range from 30 to 50 GHz, using the Mopra telescope. The spatial resolution varies from 1.0 to 1.4 arcmin and the spectral resolution from 1.6 to 2.7 km s^-1 over the frequency range. We present velocity-integrated emission images for 47 lines: 38 molecular lines and 9 radio recombination lines. There are significant differences between the distributions of different molecules, in part due to spatial differences in chemical abundance across the complex. For example, HNCO and HOCO^+ are found preferentially in the north cloud, and CH_2NH near Sgr B2 (N). Some of the differences between lines are due to excitation differences, as shown by the 36.17 and 44.07 GHz lines of CH_3OH, which have maser emission, compared to the 48.37 GHz line of CH_3OH. Other major differences in integrated molecular line distribution are due to absorption of the 7-mm free-free continuum emission (spatially traced by the radio recombination line emission) by cool intervening molecular material, causing a central dip in the molecular line distributions. These line distribution similarities and differences have been statistically described by principal component analysis (PCA), and interpreted in terms of simple Sgr B2 physical components of the cooler, lower density envelope, and dense, hot cores Sgr B2 (N), (M) and (S).
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