Some file systems allow disk storage to be allocated at different levels of granularity. for instance, a file system could allocate 8 kb of disk space as a single 8-kb block or as sixteen 512-byte blocks. how could we take advantage of this flexibility to improve performance? what modifications would have to be made to the free-space management scheme in order to support this feature?

In a heat transfer course, we can derive the equation for the temperature distribution in a flat rectangular plate. in this example, we will look at a plate at steadystate with three sides being held at t1, and one side held at t2. the temperature for any location on the plate, t(x,y), can be calculated by where create a function (prob3_5) that will take inputs of vectors x and y in feet, scalar n, scalars l and w in feet and scalars t1 and t2 in degrees fahrenheit. it will output a matrix t which is the temperature of each x and y locations. t will have the number of columns equal to the number of elements in x and rows equal to the number of elements in y. though this can be done without loops (perhaps more efficiently), your program must use a nested loop.