Math Formulas

$E = mc^2$
$\frac{\partial}{\partial t}$

$$ E = mc^2 $$

$$ \vec a=\frac{d\vec v}{dt}=\frac{d(\frac{dr}{dt}\vec e_{i}+r\frac{d\theta}{dt}\vec e_{j})}{dt}=\frac{d^2r}{dt^2}\vec e_{i}+\frac{dr}{dt}\frac{d\vec e_{i}}{dt}+\frac{dr}{dt}\frac{d\theta}{dt}\vec e_{j}+r\frac{d^2\theta}{dt^2}\vec e_{j}+r\frac{d\theta}{dt}\frac{d\vec e_{j}}{dt} $$

$$ m_t=g_t $$
$$ V_t=1 $$

$$ \eta_t=lr*{\frac {m_t}{\sqrt V_t}}=lr*g_t $$
$$ w_{t+1}=w_t-\eta_t=w_t-lr*{\frac {m_t}{\sqrt V_t}}=w_t-lr*g_t $$

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$$
q''_s = -k \left.\frac{\partial }{\partial x} (T_1+T_2) \right|_{x=0} = \underbrace{-k \left.\frac{\partial T_1}{\partial x} \right|_{x=0}}_{q''_s}  -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0} \rightarrow \boxed{0 = -k \left.\frac{\partial T_2}{\partial x} \right|_{x=0}}
$$

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$$
\begin{bmatrix}
  a & b \\
  c & d
\end{bmatrix}
$$

$$
\begin{equation}
  \left\{
    \begin{aligned}
      x=a\cos\theta\\
      y=b\sin\theta\\
    end{aligned}
  \right.
\end{equation}
$$

$$
\ce{CO2 + C -> 2 CO}
$$

$$
\begin{pmatrix}
  1 & 0 & 0 \\
  0 & 1 & 0 \\
  0 & 0 & 1
\end{pmatrix}
$$