Given the matrices $$J = \left[ {\matrix{ 3 & 2 & 1 \cr 2 & 4 & 2 \cr 1 & 2 & 6 \cr } } \right]$$ and $$K = \left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right],\,\,$$ the product $${K^T}JK$$ is ______.

For a sample of water with the ionic composition shown in the figure below, the carbonate and noncarbonate hardness concentrations (in mg/l as $${\mathrm{CaCO}}_3$$), respectively are:

Some of the nontoxic metals normally found in natural water are

A straight 100 m long raw water gravity main is to carry water from an intake structure to the jack well of a water treatment plant. The required flow through this water main is 0.21 $$m^3/s$$. Allowable velocity through the main is 0.75 m/s. Assume f = 0.01, g = 9.81 $$m/s^2$$. The minimum gradient (in cm/100m length) to be given to this gravity main so that the required amount of water flows without any difficulty is _____.