Let $$S$$ be the set containing all $$3 \times 3$$ matrices with entries from $$\{-1,0,1\}$$. The total number of matrices $$A \in S$$ such that the sum of all the diagonal elements of $$A^{\mathrm{T}} A$$ is 6 is ____________.

If the length of the latus rectum of the ellipse $$x^{2}+4 y^{2}+2 x+8 y-\lambda=0$$ is 4 , and $$l$$ is the length of its major axis, then $$\lambda+l$$ is equal to ____________.

Let $$S=\left\{z \in \mathbb{C}: z^{2}+\bar{z}=0\right\}$$. Then $$\sum\limits_{z \in S}(\operatorname{Re}(z)+\operatorname{Im}(z))$$ is equal to ______________.

A torque meter is calibrated to reference standards of mass, length and time each with $$5 \%$$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of :