Without question, yes.

Please read the book 'Square foot gardening'. This book was written with you in mind. You can plant everything you mentioned and much more in the space you have.

And don't worry about "rotating", which is needful only if you don't do an ongoing program of soil enrichment, or if your veggies are disease prone. Also, a recent report indicated that tomatoes are just fine being planted in the same area consecutive years, but while I do this, I also make a point of considerable soil renovation via the lasagna method every year. Definitely get Bartholomew's book - even old, used editions are just fine - Sq Ft gardening wastes no space, and also practices good soil management in conjunction with consecutive planting. Do put up a sturdy fence along the back of the bed and take advantage of vines - I'd suggest Fortex green beans for good taste, long production, and being nearly disease free; cucumbers also do extremely well when grown upwards. Carrots make an attractive (and tasty) edging. You should be able to grow all your salads from spring through late fall (and into the winter if you invest in row cover).