C

Evaluate the following definite integral. \[ \int\limits_0^2\left(|x-1|+1\right)\mathrm{d}x \]

Which of the following functions is increasing on the interval \([ -1;\infty)\)?

Which matrix from \(A\), \(B\), \(C\) and \(D\) does not have a determinant equal to zero? \[\] $A=\left( \array{ 1 & 2& 5\cr 1 & 3& 6\cr 1 & 4 & 7\cr } \right),$ $B=\left( \array{ 1 & 2& 3\cr 0 & 1& -1\cr 2 & 4 & 6\cr } \right),$ $C=\left( \array{ 1 & 1& 1\cr 2 & 3& 4\cr 15 & 16 & 17\cr } \right),$ $D=\left( \array{ 1 & 2& 5\cr 1 & -4& -6\cr 1 & -4 & 7\cr } \right)$

Assuming that \[ \left| \array{ 4 & 0& 2\cr a & b& c\cr 2 & 4 & 6\cr } \right|=36 \] compute the following determinant. \[ \left| \array{ 1 & 2& 3\cr a & b& c\cr 4 & 0 & 2\cr } \right| \]