We have observed the H II region RCW175 with the 64 m Parkes telescope at 8.4 GHz and 13.5 GHz in total intensity, and at 21.5 GHz in both total intensity and polarization. High angular resolution ranging from 1 to 2.4 arcmin, high sensitivity, and polarization capability enable us to perform a detailed study of the different constituents of the H II region. For the first time, we resolve three distinct regions at microwave frequencies, two of which are part of the same annular diffuse structure. Our observations enable us to confirm the presence of anomalous microwave emission (AME) from RCW175. Fitting the integrated flux density across the entire region with the currently available spinning dust models, using physically motivated assumptions, indicates the presence of at least two spinning dust components: a warm component (T gas = 5800 K) with a relatively large hydrogen number density n H = 26.3/cm3 and a cold component (T gas = 100 K) with a hydrogen number density of n H = 150/cm3. The present study is an example highlighting the potential of using high angular-resolution microwave data to break model parameter degeneracies. Thanks to the spectral coverage and angular resolution of the Parkes observations, we have been able to derive one of the first AME/excess maps, at 13.5 GHz, showing clear evidence that the bulk of the anomalous emission arises in particular from one of the source components, with some additional contribution from the diffuse structure. A cross-correlation analysis with thermal dust emission has shown a high degree of correlation with one of the regions within RCW175. In the center of RCW175, we find an average polarized emission at 21.5 GHz of 2.2 ± 0.2(rand.) ± 0.3(sys.)% of the total emission, where we have included both systematic and statistical uncertainties at 68% CL. This polarized emission could be due to sub-dominant synchrotron emission from the region and is thus consistent with very faint or non-polarized emission associated with AME.