preparation

tt1[a_, b_] := {{1, 0, 0}, {0, 1, 0}, {a, b, 1}}; 
    MatrixForm[tt1[a, b]]

rr1[θ_] := {{Cos[θ], Sin[θ], 
          0}, {-Sin[θ], Cos[θ], 0}, {0, 0, 1}}; 
    MatrixForm[rr1[θ]]

ss1[a_, b_] := {{a, 0, 0}, {0, b, 0}, {0, 0, 1}}; 
    MatrixForm[ss1[a, b]]

mm1[n_] := 
        DiagonalMatrix[
          If[n == 1, {1, -1, 1}, {-1, 1, 
              1}]];
MatrixForm[mm1[1]]
MatrixForm[mm1[2]]

example 10.7   p.247

para = {x1 -> a Cos[θ], 
          y1 -> b  Sin[θ]}/.{a -> 3, 
          b -> 
            1}    
zu1 = 
      ParametricPlot[Evaluate[{x1, y1} /. para], {θ, 0, 2  π}, 
        AspectRatio ->  1, 
        PlotRange -> {{-5, 10}, {-5, 10}}]

{x2, y2, one} = {x1, y1, 1} . tt1[2, 1] /. 
          para;
zu2 = 
      ParametricPlot[{x2, y2}, {θ, 0, 2  π}, 
        AspectRatio ->  1, 
        PlotRange -> {{-5, 10}, {-5, 10}}]

{x3, y3, one} = {x2, y2, 1} . tt1[0, 4] . ss1[2, 2] . 
          tt1[0, -4];
zu3 = 
      ParametricPlot[{x3, y3}, {θ, 0, 2  π}, 
        AspectRatio ->  1, 
        PlotRange -> {{-5, 10}, {-5, 10}}]

Show[zu1, zu2, zu3]

example 10.8   p.248

para = {x1 -> Cos[n θ] Cos[θ], 
          y1 -> 
            Cos[n θ] Sin[θ]} /. n-> 3   (*zu10  .16*) 
zu1 = 
      ParametricPlot[Evaluate[{x1, y1} /. para], {θ, 0, 2  π}, 
        AspectRatio ->  Automatic, 
        PlotRange -> {{-1, 10}, {-5, 6}}]

{x2, y2, one} = {x1, y1, 1} . tt1[2, 5] /. 
          para;
zu2 = 
      ParametricPlot[{x2, y2}, {θ, 0, 2  π}, 
        AspectRatio ->  1, 
        PlotRange -> {{-1, 10}, {-5, 6}}]

{x3, y3, one} = {x2, y2, 1} . tt1[-10, -2] . 
          rr1[60  °] . tt1[10, 2];
zu3 = 
      ParametricPlot[{x3, y3}, {θ, 0, 2  π}, 
        AspectRatio ->  1, 
        PlotRange -> {{-1, 10}, {-5, 6}}]

Show[zu1, zu2, zu3]