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本句主句为The engines would have variable nozzles;
后面是which引导的定语从句，修饰nozzles---主干为which would be fully opened...and narrowed,其中，
结果状语从句so that the exhaust would be slow and relatively quiet说明(nozzles)would be fully opened on take-off and landing情况发生时所产生的结果，现在分词结构providing the necessary speed作(nozzles)would be narrowed when the aircraft was cruising情况发生时的伴随结果，其中when时间状语从句。