A

2000017204

Level: 
A
Which of the given matrices is the matrix \((m_{i,j})\), where \(i=1, \dots, 3\) and \(j=1,~2\)?
\( \left (\array{ 8& 7\cr 6 & 5\cr 4 & 3\cr } \right ) \)
\( \left (\array{ 8& 7 & 6\cr 5 & 4 & 3\cr } \right ) \)
\( \left (\array{ 8& 7 & 6\cr 5 & 4 & 3\cr 2 & 1 & 0 } \right ) \)
\( \left (\array{ 8& 7 \cr 6 & 5 \cr } \right ) \)

2000017203

Level: 
A
Which of the given matrices have the same entry at the position \( (1,2)\)? \[ K=\left (\array{ 1& \sqrt2 & 3 & \sqrt5\cr \sqrt3& 2 & 1 & 5\cr 4& 1 & 1& 0\cr } \right ), \quad L=\left (\array{ 1& \sqrt2 & 3\cr \sqrt3 & 2 & 1\cr 4 & 1& 1\cr \sqrt5 & 5& 0 } \right ), \] \[ M=\left (\array{ \sqrt3& 2 & 1\cr \sqrt3 & 4 & 0 } \right ), \quad N=\left (\array{ 1& \sqrt3 & 4\cr \sqrt3 & 2 & 1 \cr 3 & 1 & 1 \cr \sqrt5 & 5 & 0 } \right ) \]
\(K\) and \(L\)
\(K\), \(L\) and \(N\)
\(K\), \(L\), \(M\), and \(N\)
\(L\) and \(N\)

2000017202

Level: 
A
Which of the given matrices \(K\), \(L\), \(M\), and \(N\) have the same main diagonal? \[ K=\left (\array{ 1& 7 & 8\cr 4 & 2 & 9 \cr 5 & 6 & 3 } \right ),\quad L=\left (\array{ 3& 9 & 8\cr 4 & 2 & 7 \cr 5 & 6 & 1 } \right ), \] \[ M=\left (\array{ 1& 7 & 9\cr 5 & 2 & 8 \cr 4 & 6 & 3 } \right ), \quad N=\left (\array{ 2& 7 & 8\cr 4 & 2 & 6 \cr 5 & 7 & 5 } \right ) \]
\(K\) and \(M\)
\(K\), \(L\) and \(M\)
\(K\), \(L\) and \(N\)
The main diagonals of any two matrices differ.

2000017201

Level: 
A
Which of the given matrices is of order \(3\) and has an entry of \(2\) at the position \((3,2)\)?
\[ \left (\array{ 1& 2 & 3\cr 4 & 3 & 4 \cr 3 & 2 & 1 } \right ) \]
\[ \left (\array{ 1& 2 & 3\cr 4 & 3 & 2 \cr 3 & 4 & 1 } \right ) \]
\[ \left (\array{ 1& 2 & 3\cr 4 & 3 & 2 \cr 3 & 2 & 2 \cr 1 & 2 & 3} \right ) \]
\[ \left (\array{ 1& 2 \cr 3 & 4 \cr 3 & 2 } \right ) \]

2010016709

Level: 
A
Which of the following answers contains three letters so that each letter is without a point of symmetry? (A letter has a point of symmetry if there exists a point such that the reflection through this point maps the letter into itself.)
A, U, K
S, O, H
N, U, K
A, O, H

2010016501

Level: 
A
Find the volume and the surface area of a rectangular prism with the edges of lengths \( 3\,\mathrm{cm} \), \( 9\,\mathrm{cm} \) and \( 15\,\mathrm{cm} \).
\( V= 405\,\mathrm{cm}^3 \), \( S= 414\,\mathrm{cm}^2 \)
\( V= 414\,\mathrm{cm}^3 \), \( S= 405\,\mathrm{cm}^2 \)
\( V= 415\,\mathrm{cm}^3 \), \( S= 404\,\mathrm{cm}^2 \)
\( V= 42\,\mathrm{cm}^3 \), \( S= 84\,\mathrm{cm}^2 \)