Let $\vec{a}=\langle-5,-2,2\rangle$ and $\vec{b}=\langle-2,4,1\rangle$.
Find the angle between the vectors (in degrees).

Step 1 ：Let \(\vec{a}=\langle-5,-2,2\rangle\) and \(\vec{b}=\langle-2,4,1\rangle\). We are asked to find the angle between these vectors.

Step 2 ：The angle between two vectors can be found using the dot product formula: \[\vec{a} \cdot \vec{b} = ||\vec{a}|| ||\vec{b}|| \cos(\theta)\] where \(\vec{a} \cdot \vec{b}\) is the dot product of the vectors, \(||\vec{a}||\) and \(||\vec{b}||\) are the magnitudes of the vectors, and \(\theta\) is the angle between the vectors.

Step 3 ：We can rearrange this formula to solve for \(\theta\): \[\theta = \cos^{-1}\left(\frac{\vec{a} \cdot \vec{b}}{||\vec{a}|| ||\vec{b}||}\right)\]

Step 4 ：We can calculate the dot product and the magnitudes using the given vector components. The dot product of \(\vec{a}\) and \(\vec{b}\) is 4. The magnitude of \(\vec{a}\) is approximately 5.744562646538029 and the magnitude of \(\vec{b}\) is approximately 4.58257569495584.

Step 5 ：Substituting these values into the formula, we find that the angle in radians is approximately 1.4182580376346678.

Step 6 ：Converting this angle to degrees, we find that the angle between the vectors is approximately 81.26019981697274 degrees.

Step 7 ：Final Answer: The angle between the vectors is \(\boxed{81.26}\) degrees.