Все очень просто. В предложениях со структурой there is/there are чтобы образовать вопрос is или are нужно поставить перед there. Чтобы образовать отрицание, поставить отрицательную частичку not после is или are. И все правило.
Are there many flowers in the vase? Is there a new book on the table? Отрицательная: There are not many flowers in that vase. There is not a new book on the table.
Is there a new book on the table?
Отрицательная:
There are not many flowers in that vase.
There is not a new book on the table.