<jupyter_start><jupyter_text>Math HW 1B -- Linear Algebra<jupyter_code># Prob 1<jupyter_output><empty_output><jupyter_text>The shock wave is constructed by the sharp pressure, so I assume the pressure should be maintain in the same value. $P \propto Energy / Volume = Const$. Energy itself propagates in the spherical surface with the shock wave front, so $Energy \propto t^{-2}$.So, with $Volume \propto L^{3}$, we have $t^{2} / L^{3} \Rightarrow L \propto t^{2/3}$. $L$ is the characteristic size of the shock wave.<jupyter_code># Prob 2<jupyter_output><empty_output>
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