$1.$ Suppose a sender and a receiver are $2700$ miles apart and they are communicating over a connection link with an RTT of $30$ milliseconds. The transmission rate of the link is $1\mathrm{.}2$ Gbps$.$ Suppose packet size is $1200$ bytes, including both header fields and data. $(1)$ If stop$-$and$-$wait sending is used, what is the sender$$s utilization? $(2)$ If pipelining sending is used, how many packets should the sender send in a window to achieve a channel utilization of at least $90\%?$