Take a look at the help files for functional operators.

?->

>restart:

>p:=x->7 + 6*x + x^3;

p := proc (x) options operator, arrow; 7+6*x+x^3 end proc

>q:=x->2*x^7+13*x^6-5*x^4+12*x^2+73;

q := proc (x) options operator, arrow; 2*x^7+13*x^6-5*x^4+12*x^2+73 end proc

>p(q(x));

445+12*x^7+78*x^6-30*x^4+72*x^2+(2*x^7+13*x^6-5*x^4+12*x^2+73)^3

Take a look at the examples in the help file for the command SingularValues, which is part of the LinearAlgebra package.

?LinearAlgebra[SingularValues]

Two different ways are shown.  There are others using functional notation, but this is simpler.  The display command requires loading of the plots package.

>restart:

>Gx:=.025+(x^2)/40;
>Hx:=0.006+0.5*x^2;
>Fx:=Gx+Hx;
>plot({Gx,Hx,Fx},x=0..2);

>with(plots):
>p1:=plot(Gx,x=0..2,color=blue):
>p2:=plot(Hx,x=0..2,color=green):
>p3:=plot(Fx,x=0..2,color=red):
>display(p1,p2,p3);

Partial part 2:

>solve(y=0.025+(x^2)/40,x);

>plot({(40.*y-1.)^(1/2),-1.*(40.*y-1.)^(1/2)},y=0..2.5,color=red);

A similar question was addressed in this thread not too long ago.

 This thread sounds like it addresses the same issue.

The textplot command might do it for you.  You have to load the plots package, and then use it in conjunction with the display command.  There is an example in the help files for the textplot.  To bring up the help file for this command, type the following and hit the enter key:

?textplot

If you do it with multiplication symbols, your problem should go away.  I do not use 2-D math, so I did it using the solve function.

>solve((-5.05)*(23.83-100)*c = (4.186)*(10)*(23.83-22),c);
0.1991475556

>solve((-5.05)*(c)*(23.83-100) = (4.186)*(10)*(23.83-22),c);

0.1991475556

Here is one way to do it.  Increasing the frames number will slow down the animation so you can see the drawing of the rose petal better.

>restart:

>with(plots):

>k:=7:

>animatecurve([cos(k*theta),theta,theta=0..2*Pi],frames=200,coords=polar,

numpoints=300,scaling = CONSTRAINED);
 

Greetings, Robert.  When you computed the tf from the OP, did you fix the transfer function by using a multiplication symbol (*) after the first M[tot].  Without it, it does not give your results as posted above.  This might be relevant to the OP if they are trying to recreate what you posted.

Take a look at the help file for the changecoords command.

?changecoords

Here is one way to do it:

>restart:
>with(plots):
>f:= x^2 + 5*y^2;
>cf:=contourplot(f,x=-15..15,y=-15..15,contours = 15,scaling = constrained):
>A:=[[7, 9],[5, 5]];
>pp:=pointplot(A, color = red, thickness = 3, symbol = solidcircle, symbolsize = 20):
>display(cf,pp);
 

Example below from the help files:

>restart:

>with(plots):
>animate( plot, [A*(x^2-1),x=-4..4], A=-2..2,frames=10 );

Right click on graph and select export as gif.  Changing the "frames = number" will slow it down or speed it up.
 

restart:

j:=x->1/sqrt(2*x-x^2);

j := proc (x) options operator, arrow; 1/sqrt(2*x-x^2) end proc

plot(j,0..2.5);

After looking at your expected answer, there should be a set of parentheses around the denominator as well:

>problem:=(3*x-1)/(x*(x-1));

Then the convert function will get you the answer that you are looking for.

 

 Notice the multiplication sign (*).

>restart:

>problem:=(3*x-1)/x*(x-1);

>convert(problem,parfrac,x);