A satellite of mass 2500 kg is orbiting the Earth i n an elliptical orbit. At the farthest point from the Earth, its altitude is 3600 km, while at t he nearest point, it is 1100 km. Calculate the energy and angular momentum of the satellite an d its speed at the aphelion and perihelion.

Let's start with the equations you will need for this problem.
Gravitational potential energy, U:
U= -(G*M*m)/r
where: G = gravitational constant, m = satellite's mass, and M = Earth's mass
Aphelion is where the satellite is furthest away:
r_1= R_E + 3600 km=9.967*10^6 m
Perihelion is where the satellite is the closest:
r_2= R_E + 1100 km=7.467*10^6 m
Conservation of Energy:
K_1+U_1 = K_2+U_2
1/2*m*v_1^2-G*m*M/r_1=1/2*m*v_2^2-G*m*M/r_2
Conservation of Angular Momentum:
mv_1 r_1=mv_2 r_2
Solve system of equations for v2.
1/2*m*(v_2*r_2/r_1)^2-G*m*M/r_1=1/2*m*v_2^2-G*m*M/r_2
v_2^2 = 2GM*(1/r_1-1/r_2)/((r_2/r_1)^2-1)
Plug in numerical values to and solve to get the velocities. 
v_1 = 4387.3 m/s at aphelion, and 5856.2 m/s at perihelion.
Next, plug in either position 1 or position 2 values to get E at BOTH aphelion and perihelion of E=K+U=1/2*m*v_1^2-G*m*M/r_1=7.603*10^10 J
Your angular momentum will also be the same for both aphelion and perihelion
J=m*r_1*v_1=1.09x10^14 (kgm^2)/s
Therefore this problem was completly solved by the conservation of energy and angular momentum.
I included a link that attempts to solve this same problem in more detail. There numerical values are incorrect because they are missing a factor of two when they solve for the velocity.
https://www.assignmentexpert.com/homework-answers/physics-Answer-61340.pdf