I was having a hard time understanding and solving this question that wants me to show the final tape and figuring out if whether or not the turning machine accepts it or not. I have a list of 20 problems, that I want to solve to prepare for my interview at Mathworks, and the if any of you can help me solve these 2, I will solve the remaining on my own. An explanation would help.
Does the TM accept
A)101010 B)00100 The turing machine is here,

And to design a turing machine that accepts {a^2n : n>0}
I appreciate your help, I really want to learn it, and I learn by examples, thanks.
Thank you