old exam #1:
photon1: x=ct
photon2: x=ct+L

photon1: gamma*(x'+beta ct')=gamma*(beta x'+ct')
	     x'*(1-beta) = ct'(1-beta)
                   x'=ct' (thru origina at t'=0)

photon2: gamma*(x'+beta ct')=gamma*(beta x'+ct') +L
               x'*(1-beta) = ct'(1-beta)+L/gamma
			x' =ct' +L/gamma/(1-beta)
                        x'=ct' + L sqrt((1+beta)/(1-beta))


old exam #7
space ship start (just reading chart): (-1.9,-1.9), (-2.2,+.9), note that it moved backwards (v'<0)
given that gamma=1.1 we can make an exact calculation:
In[1]:= gamma=1.1                                                                                              

Out[1]= 1.1

In[2]:= beta=Sqrt[1-1/gamma^2]                                                                                 

Out[2]= 0.416598

In[3]:= m={{gamma, -beta gamma},{-beta gamma, gamma}}                                                          

Out[3]= {{1.1, -0.458258}, {-0.458258, 1.1}}

In[4]:= m.{-3,-3}                                                                                              

Out[4]= {-1.92523, -1.92523}

In[5]:= m.{-2,0}                                                                                               

Out[5]= {-2.2, 0.916515}

remark: we can calculate the velocity and compare to the velocity addition formula:

In[7]:= (-2.2+1.92523)/(0.916515+1.92523)                                                                      

Out[7]= -0.0966906

In[8]:= (1/3-beta)/(1-beta*(1/3))                                                                              

Out[8]= -0.0966916