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pretraining/mathematica/linear_algebra/dot_product/11978.txt

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+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 0 \\
+ -3 \pi  \\
+ -\pi  \\
+ 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 3 \pi  \\
+ 0 \\
+ -2 \pi  \\
+ \pi  \\
+\end{array}
+\right)$.
+Answer:
+$2 \pi ^2$

pretraining/mathematica/linear_algebra/dot_product/12529.txt

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+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ \pi  \\
+ 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 2 \pi  \\
+ -2 \pi  \\
+\end{array}
+\right)$.
+Answer:
+$2 \pi ^2$

pretraining/mathematica/linear_algebra/dot_product/12958.txt

@@ -0,0 +1,22 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -7 \\
+ 1 \\
+ \frac{3}{2} \\
+ 2 \\
+ -8 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{17}{2} \\
+ -8 \\
+ -6 \\
+ -\frac{17}{2} \\
+ -10 \\
+\end{array}
+\right)$.
+Answer:
+$-\frac{27}{2}$

pretraining/mathematica/linear_algebra/dot_product/13268.txt

@@ -0,0 +1,18 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -4 \\
+ 4 \\
+ -7 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -3 \\
+ 4 \\
+ -9 \\
+\end{array}
+\right)$.
+Answer:
+$91$

pretraining/mathematica/linear_algebra/dot_product/14207.txt

@@ -0,0 +1,24 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -\frac{9}{2} \\
+ \frac{11}{2} \\
+ \frac{1}{2} \\
+ 5 \\
+ \frac{13}{2} \\
+ -\frac{5}{2} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -8 \\
+ \frac{1}{2} \\
+ -7 \\
+ \frac{15}{2} \\
+ -\frac{7}{2} \\
+ -6 \\
+\end{array}
+\right)$.
+Answer:
+$65$

pretraining/mathematica/linear_algebra/dot_product/14256.txt

@@ -0,0 +1,28 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 9 \\
+ 6 \\
+ 1 \\
+ 6 \\
+ -9 \\
+ 6 \\
+ -2 \\
+ 8 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 7 \\
+ 8 \\
+ 3 \\
+ 5 \\
+ 6 \\
+ 6 \\
+ -7 \\
+ -2 \\
+\end{array}
+\right)$.
+Answer:
+$124$

pretraining/mathematica/linear_algebra/dot_product/15079.txt

@@ -0,0 +1,20 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 5 \\
+ 1 \\
+ -2 \\
+ -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 5 \\
+ 0 \\
+ 4 \\
+ 1 \\
+\end{array}
+\right)$.
+Answer:
+$15$

pretraining/mathematica/linear_algebra/dot_product/15184.txt

@@ -0,0 +1,28 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ \frac{11}{\sqrt{3}} \\
+ 0 \\
+ 5 \sqrt{3} \\
+ \frac{4}{\sqrt{3}} \\
+ 4 \sqrt{3} \\
+ \frac{17}{\sqrt{3}} \\
+ \frac{13}{\sqrt{3}} \\
+ \frac{10}{\sqrt{3}} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{17}{\sqrt{3}} \\
+ -\frac{7}{\sqrt{3}} \\
+ \frac{13}{\sqrt{3}} \\
+ \frac{13}{\sqrt{3}} \\
+ 0 \\
+ \frac{5}{\sqrt{3}} \\
+ \frac{14}{\sqrt{3}} \\
+ -2 \sqrt{3} \\
+\end{array}
+\right)$.
+Answer:
+$\frac{641}{3}$

pretraining/mathematica/linear_algebra/dot_product/15658.txt

@@ -0,0 +1,18 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -8 \\
+ 9 \\
+ -8 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 7 \\
+ 2 \\
+ -2 \\
+\end{array}
+\right)$.
+Answer:
+$-22$

pretraining/mathematica/linear_algebra/dot_product/16259.txt

@@ -0,0 +1,26 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -7 \\
+ -9 \\
+ -1 \\
+ 7 \\
+ -1 \\
+ 1 \\
+ -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 9 \\
+ 1 \\
+ 6 \\
+ 6 \\
+ 8 \\
+ 9 \\
+ -9 \\
+\end{array}
+\right)$.
+Answer:
+$-17$

pretraining/mathematica/linear_algebra/dot_product/16266.txt

@@ -0,0 +1,28 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 3 \sqrt{5} \\
+ \sqrt{5} \\
+ 4 \sqrt{5} \\
+ -2 \sqrt{5} \\
+ -2 \sqrt{5} \\
+ -4 \sqrt{5} \\
+ -2 \sqrt{5} \\
+ -4 \sqrt{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -2 \sqrt{5} \\
+ 4 \sqrt{5} \\
+ -\sqrt{5} \\
+ -3 \sqrt{5} \\
+ -3 \sqrt{5} \\
+ -4 \sqrt{5} \\
+ \sqrt{5} \\
+ 0 \\
+\end{array}
+\right)$.
+Answer:
+$100$

pretraining/mathematica/linear_algebra/dot_product/17031.txt

@@ -0,0 +1,22 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 7 \\
+ -2 \\
+ 3 \\
+ -3 \\
+ -2 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -1 \\
+ -5 \\
+ -9 \\
+ -1 \\
+ -8 \\
+\end{array}
+\right)$.
+Answer:
+$-5$

pretraining/mathematica/linear_algebra/dot_product/18547.txt

@@ -0,0 +1,20 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -\frac{19}{3} \\
+ -6 \\
+ \frac{29}{3} \\
+ 5 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -1 \\
+ -\frac{28}{3} \\
+ -4 \\
+ 0 \\
+\end{array}
+\right)$.
+Answer:
+$\frac{71}{3}$

pretraining/mathematica/linear_algebra/dot_product/2120.txt

@@ -0,0 +1,16 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 9 \\
+ 10 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 7 \\
+ -8 \\
+\end{array}
+\right)$.
+Answer:
+$-17$

pretraining/mathematica/linear_algebra/dot_product/23501.txt

@@ -0,0 +1,28 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 4 \\
+ -1 \\
+ 8 \\
+ 2 \\
+ -3 \\
+ -6 \\
+ 2 \\
+ 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -10 \\
+ -9 \\
+ -7 \\
+ 6 \\
+ 3 \\
+ -8 \\
+ 2 \\
+ -4 \\
+\end{array}
+\right)$.
+Answer:
+$-32$

pretraining/mathematica/linear_algebra/dot_product/23774.txt

@@ -0,0 +1,20 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -2 e \\
+ -3 e \\
+ -2 e \\
+ -2 e \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 3 e \\
+ -3 e \\
+ e \\
+ -3 e \\
+\end{array}
+\right)$.
+Answer:
+$7 e^2$

pretraining/mathematica/linear_algebra/dot_product/25173.txt

@@ -0,0 +1,24 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -6 \\
+ 5 \\
+ 8 \\
+ 4 \\
+ 5 \\
+ -5 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 0 \\
+ -3 \\
+ -9 \\
+ 7 \\
+ 1 \\
+ -10 \\
+\end{array}
+\right)$.
+Answer:
+$-4$

pretraining/mathematica/linear_algebra/dot_product/26645.txt

@@ -0,0 +1,28 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -4 \\
+ -8 \\
+ 0 \\
+ -8 \\
+ -3 \\
+ -8 \\
+ 0 \\
+ 8 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 0 \\
+ -9 \\
+ 8 \\
+ -7 \\
+ -6 \\
+ -5 \\
+ 5 \\
+ 6 \\
+\end{array}
+\right)$.
+Answer:
+$234$

pretraining/mathematica/linear_algebra/dot_product/26742.txt

@@ -0,0 +1,16 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -4 \sqrt{3} \\
+ 6 \sqrt{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -3 \sqrt{3} \\
+ -4 \sqrt{3} \\
+\end{array}
+\right)$.
+Answer:
+$-36$

pretraining/mathematica/linear_algebra/dot_product/28228.txt

@@ -0,0 +1,18 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 4 \sqrt{5} \\
+ 3 \sqrt{5} \\
+ 3 \sqrt{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -\sqrt{5} \\
+ 3 \sqrt{5} \\
+ 4 \sqrt{5} \\
+\end{array}
+\right)$.
+Answer:
+$85$

pretraining/mathematica/linear_algebra/dot_product/28310.txt

@@ -0,0 +1,24 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -4 \\
+ -6 \\
+ -5 \\
+ -7 \\
+ 7 \\
+ 10 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 0 \\
+ -1 \\
+ -4 \\
+ 6 \\
+ -4 \\
+ 8 \\
+\end{array}
+\right)$.
+Answer:
+$36$

pretraining/mathematica/linear_algebra/dot_product/28737.txt

@@ -0,0 +1,26 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -7.106 \\
+ -9.901 \\
+ -2.415 \\
+ -3.921 \\
+ 2.264 \\
+ -8.933 \\
+ 1.64 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 6.616 \\
+ 8.052 \\
+ -5.11 \\
+ -0.828 \\
+ 2.741 \\
+ -7.143 \\
+ -1.53 \\
+\end{array}
+\right)$.
+Answer:
+$-43.6441$

pretraining/mathematica/linear_algebra/dot_product/30701.txt

@@ -0,0 +1,28 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 8.87 \\
+ -5.548 \\
+ 1.823 \\
+ 6.997 \\
+ -9.845 \\
+ -5.864 \\
+ 3.14 \\
+ -9.54 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -1.913 \\
+ -6.705 \\
+ -7.194 \\
+ 9.792 \\
+ -3.397 \\
+ -4.76 \\
+ 1.432 \\
+ -3.143 \\
+\end{array}
+\right)$.
+Answer:
+$171.468$

pretraining/mathematica/linear_algebra/dot_product/31538.txt

@@ -0,0 +1,14 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ \frac{36}{5} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -\frac{37}{5} \\
+\end{array}
+\right)$.
+Answer:
+$-\frac{1332}{25}$

pretraining/mathematica/linear_algebra/dot_product/33860.txt

@@ -0,0 +1,20 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -\frac{13}{\sqrt{3}} \\
+ -5 \sqrt{3} \\
+ 4 \sqrt{3} \\
+ -\frac{16}{\sqrt{3}} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -\frac{14}{\sqrt{3}} \\
+ -\frac{7}{\sqrt{3}} \\
+ -\frac{13}{\sqrt{3}} \\
+ \frac{4}{\sqrt{3}} \\
+\end{array}
+\right)$.
+Answer:
+$\frac{67}{3}$

pretraining/mathematica/linear_algebra/dot_product/3390.txt

@@ -0,0 +1,16 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -7 \\
+ -6 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 1 \\
+ -6 \\
+\end{array}
+\right)$.
+Answer:
+$29$

pretraining/mathematica/linear_algebra/dot_product/33931.txt

@@ -0,0 +1,26 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -5 \\
+ -10 \\
+ -9 \\
+ -1 \\
+ -9 \\
+ -6 \\
+ 7 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -4 \\
+ -3 \\
+ 6 \\
+ 0 \\
+ 7 \\
+ -7 \\
+ 9 \\
+\end{array}
+\right)$.
+Answer:
+$38$

pretraining/mathematica/linear_algebra/dot_product/34849.txt

@@ -0,0 +1,14 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 4 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -5 \\
+\end{array}
+\right)$.
+Answer:
+$-20$

pretraining/mathematica/linear_algebra/dot_product/34987.txt

@@ -0,0 +1,22 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 5.8 \\
+ -5.5 \\
+ -5.7 \\
+ 3.5 \\
+ 7.6 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 3.6 \\
+ 7.5 \\
+ -6.6 \\
+ -2. \\
+ -6.7 \\
+\end{array}
+\right)$.
+Answer:
+$-40.67$

pretraining/mathematica/linear_algebra/dot_product/35344.txt

@@ -0,0 +1,20 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -2 \pi  \\
+ -3 \pi  \\
+ 0 \\
+ \pi  \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 0 \\
+ 0 \\
+ \pi  \\
+ -3 \pi  \\
+\end{array}
+\right)$.
+Answer:
+$-3 \pi ^2$

pretraining/mathematica/linear_algebra/dot_product/35647.txt

@@ -0,0 +1,28 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -\frac{18}{e} \\
+ \frac{17}{e} \\
+ \frac{24}{e} \\
+ \frac{7}{e} \\
+ \frac{7}{e} \\
+ \frac{17}{e} \\
+ -\frac{18}{e} \\
+ \frac{26}{e} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{25}{e} \\
+ -\frac{1}{e} \\
+ \frac{10}{e} \\
+ \frac{8}{e} \\
+ -\frac{22}{e} \\
+ -\frac{3}{e} \\
+ \frac{11}{e} \\
+ \frac{23}{e} \\
+\end{array}
+\right)$.
+Answer:
+$\frac{24}{e^2}$

pretraining/mathematica/linear_algebra/dot_product/37230.txt

@@ -0,0 +1,14 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ \frac{18}{e} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -\frac{26}{e} \\
+\end{array}
+\right)$.
+Answer:
+$-\frac{468}{e^2}$

pretraining/mathematica/linear_algebra/dot_product/37354.txt

@@ -0,0 +1,22 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -6 \sqrt{3} \\
+ -2 \sqrt{3} \\
+ 5 \sqrt{3} \\
+ 0 \\
+ \sqrt{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -3 \sqrt{3} \\
+ 3 \sqrt{3} \\
+ -2 \sqrt{3} \\
+ -\sqrt{3} \\
+ -2 \sqrt{3} \\
+\end{array}
+\right)$.
+Answer:
+$0$

pretraining/mathematica/linear_algebra/dot_product/39521.txt

@@ -0,0 +1,18 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ \sqrt{3} \\
+ \frac{8}{\sqrt{3}} \\
+ -\frac{17}{\sqrt{3}} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{11}{\sqrt{3}} \\
+ -5 \sqrt{3} \\
+ -\frac{5}{\sqrt{3}} \\
+\end{array}
+\right)$.
+Answer:
+$-\frac{2}{3}$

pretraining/mathematica/linear_algebra/dot_product/41059.txt

@@ -0,0 +1,26 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 2 \\
+ -4 \\
+ 8 \\
+ -3 \\
+ 2 \\
+ -10 \\
+ 4 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 1 \\
+ 9 \\
+ -3 \\
+ 5 \\
+ -8 \\
+ -4 \\
+ -2 \\
+\end{array}
+\right)$.
+Answer:
+$-57$

pretraining/mathematica/linear_algebra/dot_product/41454.txt

@@ -0,0 +1,20 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -4 \\
+ -8 \\
+ -5 \\
+ -6 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -8 \\
+ 5 \\
+ 5 \\
+ -8 \\
+\end{array}
+\right)$.
+Answer:
+$15$

pretraining/mathematica/linear_algebra/dot_product/41818.txt

@@ -0,0 +1,24 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -10 \\
+ -\frac{48}{5} \\
+ -\frac{34}{5} \\
+ -\frac{19}{5} \\
+ -\frac{33}{5} \\
+ 3 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 10 \\
+ -\frac{14}{5} \\
+ 6 \\
+ -\frac{36}{5} \\
+ -\frac{49}{5} \\
+ \frac{21}{5} \\
+\end{array}
+\right)$.
+Answer:
+$-\frac{232}{25}$

pretraining/mathematica/linear_algebra/dot_product/4282.txt

@@ -0,0 +1,22 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 8 \\
+ -5 \\
+ -8 \\
+ -3 \\
+ -9 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -8 \\
+ 1 \\
+ -6 \\
+ 4 \\
+ 3 \\
+\end{array}
+\right)$.
+Answer:
+$-60$

pretraining/mathematica/linear_algebra/dot_product/43819.txt

@@ -0,0 +1,22 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 8 \\
+ -\frac{19}{3} \\
+ 5 \\
+ -\frac{8}{3} \\
+ -\frac{19}{3} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ \frac{20}{3} \\
+ -\frac{26}{3} \\
+ \frac{22}{3} \\
+ 1 \\
+ 7 \\
+\end{array}
+\right)$.
+Answer:
+$\frac{881}{9}$

pretraining/mathematica/linear_algebra/dot_product/43909.txt

@@ -0,0 +1,24 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 7 \\
+ 8 \\
+ 2 \\
+ -2 \\
+ 5 \\
+ 8 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 8 \\
+ -4 \\
+ -2 \\
+ 5 \\
+ -9 \\
+ -4 \\
+\end{array}
+\right)$.
+Answer:
+$-67$

pretraining/mathematica/linear_algebra/dot_product/43937.txt

@@ -0,0 +1,22 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -5 \\
+ -8 \\
+ 4 \\
+ 3 \\
+ -9 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -4 \\
+ -7 \\
+ 7 \\
+ 1 \\
+ -2 \\
+\end{array}
+\right)$.
+Answer:
+$125$

pretraining/mathematica/linear_algebra/dot_product/4406.txt

@@ -0,0 +1,14 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -6 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 4 \\
+\end{array}
+\right)$.
+Answer:
+$-24$

pretraining/mathematica/linear_algebra/dot_product/44695.txt

@@ -0,0 +1,26 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -10 \\
+ -5 \\
+ 0 \\
+ 5 \\
+ 4 \\
+ -7 \\
+ 7 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -8 \\
+ -4 \\
+ -8 \\
+ -7 \\
+ 4 \\
+ -9 \\
+ 3 \\
+\end{array}
+\right)$.
+Answer:
+$165$

pretraining/mathematica/linear_algebra/dot_product/48187.txt

@@ -0,0 +1,24 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -5 \\
+ -8 \\
+ 3 \\
+ -3 \\
+ -8 \\
+ 0 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 2 \\
+ 8 \\
+ -5 \\
+ 2 \\
+ -3 \\
+ 0 \\
+\end{array}
+\right)$.
+Answer:
+$-71$

pretraining/mathematica/linear_algebra/dot_product/48706.txt

@@ -0,0 +1,28 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -3 \log (2) \\
+ 14 \log (2) \\
+ 3 \log (2) \\
+ -13 \log (2) \\
+ 12 \log (2) \\
+ \log (2) \\
+ -8 \log (2) \\
+ -2 \log (2) \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -8 \log (2) \\
+ -12 \log (2) \\
+ 11 \log (2) \\
+ -8 \log (2) \\
+ -2 \log (2) \\
+ -12 \log (2) \\
+ 14 \log (2) \\
+ 3 \log (2) \\
+\end{array}
+\right)$.
+Answer:
+$-161 \log ^2(2)$

pretraining/mathematica/linear_algebra/dot_product/6046.txt

@@ -0,0 +1,20 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ \frac{11}{2} \\
+ -1 \\
+ \frac{1}{2} \\
+ \frac{1}{2} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 5 \\
+ -\frac{7}{2} \\
+ 7 \\
+ 3 \\
+\end{array}
+\right)$.
+Answer:
+$36$

pretraining/mathematica/linear_algebra/dot_product/801.txt

@@ -0,0 +1,28 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -\frac{11}{\sqrt{2}} \\
+ \frac{9}{\sqrt{2}} \\
+ 5 \sqrt{2} \\
+ -\sqrt{2} \\
+ -\frac{7}{\sqrt{2}} \\
+ -\sqrt{2} \\
+ \frac{9}{\sqrt{2}} \\
+ -\frac{3}{\sqrt{2}} \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ -\sqrt{2} \\
+ \frac{7}{\sqrt{2}} \\
+ -\sqrt{2} \\
+ -\frac{5}{\sqrt{2}} \\
+ -\frac{5}{\sqrt{2}} \\
+ \sqrt{2} \\
+ \frac{1}{\sqrt{2}} \\
+ \frac{9}{\sqrt{2}} \\
+\end{array}
+\right)$.
+Answer:
+$44$

pretraining/mathematica/linear_algebra/dot_product/9381.txt

@@ -0,0 +1,16 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ -9 \\
+ -5 \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 7 \\
+ 3 \\
+\end{array}
+\right)$.
+Answer:
+$-78$

pretraining/mathematica/linear_algebra/dot_product/9512.txt

@@ -0,0 +1,14 @@
+Problem:
+Find the dot product of the following two vectors:
+$\left(
+\begin{array}{c}
+ 2 \log (2) \\
+\end{array}
+\right)$ and
+$\left(
+\begin{array}{c}
+ 6 \log (2) \\
+\end{array}
+\right)$.
+Answer:
+$12 \log ^2(2)$

pretraining/mathematica/number_theory/multiplicative_order/10170.txt

@@ -0,0 +1,4 @@
+Problem:
+Find the smallest integer $m$ such that $103^m \equiv 1 \pmod{295}$.
+Answer:
+$116$