RadiusDistribution = NormalDistribution[0, 1];
AngleDistribution = UniformDistribution[{0, Pi}];

(*Mathematica has built in transformation functions, but this seems clearer given the way the instructions were written.*)
ToCartesian[{r_, a_}] := ToCartesian[{Abs@r, a - Pi}] /; Negative[r];
ToCartesian[{r_, a_}] := FromPolarCoordinates[{r, a}];

newData =
  ToCartesian /@
   Transpose[{RandomVariate[RadiusDistribution, 100],
     RandomVariate[AngleDistribution, 100]}];

TableForm[Results[#, newData] & /@ Range[4], TableSpacing -> 5]