diff --git a/cs223a-homework-5.tex b/cs223a-homework-5.tex
index 4dd96c1..dab3207 100644
--- a/cs223a-homework-5.tex
+++ b/cs223a-homework-5.tex
@@ -145,8 +145,8 @@
 \begin{equation}
   \prescript{0}{C_2}T =
     \begin{bmatrix}
-      c\theta & s\theta  & 0 & L_1c\theta \\
-      s\theta & -c\theta & 0 & L_1s\theta \\
+      c\theta & -s\theta & 0 & L_1c\theta \\
+      s\theta & c\theta  & 0 & L_1s\theta \\
       0       & 0        & 1 & d_2        \\
       0       & 0        & 0 & 1          \\
     \end{bmatrix}
@@ -212,7 +212,7 @@
 
 \begin{equation}
   \prescript{C_1}{}I_1 = \begin{bmatrix}
-    \frac{m_1}{12}2h^2                         & 0             & 0           \\
+    \frac{m_1}{6}h^2                           & 0             & 0           \\
     0                & \frac{m_1}{12}(L_1^2 + h^2)             & 0           \\
     0                & 0                       & \frac{m_1}{12}(L_1^2 + h^2) \\
                          \end{bmatrix}
@@ -236,7 +236,7 @@
   \prescript{C_2}{}I_2 = \begin{bmatrix}
     \frac{m_2}{12}(L_2^2 + h^2)                & 0             & 0           \\
     0                & \frac{m_2}{12}(L_2^2 + h^2)             & 0           \\
-    0                & 0                       & \frac{m_2}{12}2h^2          \\
+    0                & 0                       & \frac{m_2}{6}h^2            \\
                          \end{bmatrix}
 \end{equation}
 
@@ -246,7 +246,7 @@
 
 \begin{equation}
   J_{v1}^T J_{v1} = \begin{bmatrix}
-    \frac{L_1}{4} & 0 \\
+    \frac{L_1^2}{4} & 0 \\
     0             & 0 \\
                     \end{bmatrix}
 \end{equation}
@@ -298,7 +298,7 @@
 
 \part
 
-The joints positions do not affect the centrifugal and inertia along the first joint axis, so at the end, the result will be null. Let's try to develop the equation anyhow.
+The joints positions do not affect the centrifugal and inertia along the first joint axis, so at the end, the result will be null. Let's try to develop the equation anyway.
 
 \begin{equation}
   v = \begin{bmatrix}
@@ -437,7 +437,7 @@
 \begin{subequations}
   \begin{equation}
     \tau_1 = (L_1^2 \frac{m_1}{3} + h^2 \frac{m_1}{12} + L_1^2 m_2
-             + h^2 \frac{m_2}{6}) \ddot \Theta
+             + h^2 \frac{m_2}{6}) \ddot \theta_1
   \end{equation}
   \begin{equation}
     \tau_2 = m_2 \ddot d_2 + m_2 g